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Calhoun: The NPS Institutional Archive
Reports and Technical Reports All Technical Reports Collection
2000-06
Computer modeling and simulation of bullet
impact to the human thorax
Jolly, Johannes E.
http://hdl.handle.net/10945/48955
NPS-ME-00-002
NAVAL POSTGRADUATE SCHOOL
Prepared for:
Monterey, California
COMPUTER MODELING AND SIMULATION OF BULLET IMP ACT TO THE HUMAN THORAX
by
Johannes E. Jolly and
Young W. Kwon
July 1999 - June 2000
Approved for public release; distribution is unlimited.
Headquarters, U.S. Army Soldier & Biological Chemical Command Soldier Systems Center Attn: AMSSB-SRM-PB-B(N) Natick, MA 01760-5021
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NAVAL POSTGRADUATE SCHOOL Monterey, California 93943
RADM RICHARD H. WELLS Superintendent
R. S. ELSTER Provost
This thesis was prepared in conjunction with research sponsored in part by Headquarters, U.S. Army Soldier & Biological Chemical Command, Soldier Systems Center, Natick, MA.
Reproduction of all or part of this report is authorized.
This report was prepared by:
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-Chairman Department of Mechanical Engineering
Professor of Mechanical Engineering
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4. TITLE AND SUBTITLE: 5. FUNDING NUMBERS
Computer Modeling and Simulation of Bullet Impact to the Human Thorax
6. AUTHOR(S) MIPR 9MS6R99631 Jolly, Johannes E. and Kwon, Young W.
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION Naval Postgraduate School REPORT NUMBER Monterey CA 93943-5000 NPS-ME-00-002
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING Headquarters, U.S. Army Soldier & Biological Chemical Command, Soldier Systems Center, AGENCY REPORT NUMBER Attn: AMSSB-SRM-PB-B(N), Kansas Street, Natick, MA 01760-5021
11. SUPPLEMENTARY NOTES The views expressed here are those of the authors and do not reflect the official policy or position of the Department of Defense or the U.S. Government.
12a. DISTRIBUTION/ AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Approved for public release; distribution is unlimited. A
13. ABSTRACT (maximum 200 words) The biomechanical response of a finite element model of the human thorax and a protective body armor system was studied under impact loading from a projectile. The objective of the study was to create a viable finite element model of the human thorax. The model was validated by comparing the results of tests of body armor systems conducted on cadavers to results obtained from finite element analysis. A parametric study was undertaken to determine the essential components of the model. The results from this investigation determined that the path of force propagation from a body armor system to the thorax upon bullet impact is directly through the vest to the sternum and then through the skeleton to the rest of the body. Thus, any parameters that affect the components in this pathway were essential to the model. This included the muscles, their geometries, material properties, and viscosity, as well as the Young's modulus of the sternochondral cartilage and the bones themselves.
14. SUBJECT TERMS Finite Element Analysis, Human Thorax Model, Impact Analysis
17. SECURITY 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION OF REPORT OF THIS PAGE CLASSIFICATION OF
Unclassified Unclassified ABSTRACT Unclassified
NSN 7540-01-280-5500
15. NUMBER OF PAGES 131
16. PRICE CODE
20. LIMITATION OF ABSTRACT
UL
Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. 239-18 298-102
11
ABSTRACT
The biomechanical response of a finite element model of the human thorax and a
protective body armor system was studied under impact loading from a projectile. The
objective of the study was to create a viable finite element model of the human thorax.
The model was validated by comparing the results of tests of body armor systems
conducted on cadavers to results obtained from finite element analysis. A parametric
study was undertaken to determine the essential components of the model. The results
from this investigation determined that the path of force propagation from a body armor
system to the thorax upon bullet impact is directly through the vest to the sternum and
then through the skeleton to the rest of the body. Thus, any parameters that affect the
components in this pathway were essential to the model. This included the muscles, their
geometries, material properties, and viscosity, as well as the Young's modulus of the
stemochondral cartilage and the bones themselves.
iii
IV
TABLE OF CONTENTS
I. INTRODUCTION .................................................................................................. 1
II. BACKGROUND .................................................................................................... 3
A. FINITE ELEMENT ANALYSIS ............................................................... 3
1. Introduction to Finite Element Analysis ......................................... 3
2. History of Finite Element Analysis ................................................. 3
3. How the Method Works .................................................................. 5
4. Range of Applications ..................................................................... 9
B. PROPERTIES OF BONE ......................................................................... 10
C. PROPERTIES OF CARTILAGE ............................................................. 17
D. ANATOMYOFTHORAX ...................................................................... 19
1. Spine ............................................................................................. 20
2. Ribs .............................................................................................. 24
3. Sternum ......................................................................................... 26
4. Costal Cartilage ............................................................................. 27
E. BODY ARMOR ........................................................................................ 28
1. A History of Body Armor ............................................................. 28
2. Armor Classification ..................................................................... 29
3. Classification Requirements: ........................................................ 33
a. Wet Testing ....................................................................... 33
b. Angle Shots ....................................................................... 34
v
c. Performance Testing ......................................................... 34
d. V50 Testing ....................................................................... 36
4. Body Armor Construction ............................................................. 37
a. Methods of Construction ................................................... 39
b. Materials Used .................................................................. 39
F. LITERATURE SURVEY ......................................................................... 41
III. FINITE ELEMENT MODEL ............................................................................... 45
A. HUMAN THORACIC BODY MODEL .................................................. 45
1. Ribs ............................................................................................... 45
2. Spine ............................................................................................. 46
3. Sternum ......................................................................................... 48
4. Muscle ........................................................................................... 49
5. Cartilage ........................................................................................ 50
B. BODY ARMOR ........................................................................................ 52
C. INTERFACE ELEMENTS ....................................................................... 53
D. PROJECTILE ........................................................................................... 54
E. BOUNDARY CONDITIONS .................................................................. 55
F. ANALYSIS CODE ................................................................................... 56
IV. RESULTS AND DISCUSSION ........................................................................... 57
A. VIABILITY STUDY ....................................................................................... 58
1. CBA Plate, Kevlar Vest, and NATO 7.62mm ball M80 Round ... 58
2. Kevlar Vest and NA TO 9mm Round ............................................ 64
vi
B. PARAMETRIC STUDY .......................................................................... 69
V. CONCLUSIONS/RECOMMENDATIONS ......................................................... 85
A. CONCLUSIONS ....................................................................................... 85
B. RECOMMENDATIONS .......................................................................... 86
LIST OF REFERENCES .................................................................................................. 89
APPENDIX A: PARAMETRIC STUDY RESULTS ...................................................... 91
APPENDIX B: VISCOELASTIC SOLIDS .................................................................... 107
INITIAL DISTRIBUTION LIST ................................................................................... 113
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Vlll
LIST OF FIGURES
Figure 1: Discretization of a Tapered Rod. From Ref. [2]. ................................................ 5
Figure 2: Discretization of a Plate Member. From Ref. [2]. ............................................. 6
Figure 3: Elements having Shape Distortions that Tend to Promote Poor Results. From
Ref. [2] .............................................................................................................. 8
Figure 4: Eight Noded Brick Element. From Ref. [2]. ..................................................... 8
Figure 5: Twenty-Noded Brick Element. From Ref. [5]. .................................................. 8
Figure 6: Human Skeleton. From Ref. [7]. ..................................................................... 11
Figure 7: Long Bone. From Ref. [6] ............................................................................... 12
Figure 8: Cross-section of Compact Bone. From Ref. [7]. ............................................. 14
Figure 9: Basic Structure of Compact Bone. Original from Ham (1969). From Ref. [6].
························································································································· 15
Figure 10: Stress-Strain Curves of Human Femur. Original From Evans (1969). From
Ref. [6] ............................................................................................................ 16
Figure 11: Sternum and Costal Cartilages. From Ref. [7] .............................................. 20
Figure 12: Vertebral Column. From Ref. [7]. .................................................................. 21
Figure 13: Lumbar Vertebra. From Ref. [7] ................................................................... 21
Figure 14: Cervical Vertebra. From Ref. [7]. ................................................................. 21
Figure 15: Thoracic Vertebra (Superior and Lateral Aspects). From Ref. [7]. .............. 23
Figure 16: Ninth, Tenth, and Eleventh Vertebrae. From Ref. [7]. .................................. 23
lX
Figure 17: (a) Fifth Rib, Inferior Aspect; (b) Fifth Rib, Posterior Aspect; (c) First Rib.
From Ref. [7] .................................................................................................. 25
Figure 18: Posterior Aspect of the Sternum. From Ref. (8) ............................................ 27
Figure 19: Range Set-up for Test Firings. From Ref. [12]. ............................................. 35
Figure 20: Impact Locations for NIJ Testing. From Ref. [12). ........................................ 35
Figure 21: Plot of Sternum, Ribs, Spine, and Cartilage ................................................... 46
Figure 22: Medial View of the Ribs and Spine ................................................................ 48
Figure 23: Sternum Shape in Thorax Model.. .................................................................. 49
Figure 24: Muscle as Constructed in Thorax Model ....................................................... 50
Figure 25: Articular Cartilage Connecting Sternum and Ribs ......................................... 51
Figure 26: Depiction of Kevlar Vest Overlaying Muscle ................................................ 53
Figure 27: Medial View of CBA Plate and Kevlar Vest ................................................. 55
Figure 28: Sternum Acceleration (CBA & Kevlar). After Ref. [13]. ............................. 59
Figure 29: Sternum Velocity (CBA & Kevlar). After Ref. [13]. ..................................... 61
Figure 30: Sternum Displacements (CBA & Kevlar). After Ref. [13]. ........................... 61
Figure 31: Spinal Acceleration (CBA & Kevlar). After Ref. [13). .................................. 63
Figure 32: Spinal Velocity (CBA & Kevlar). After Ref. [13]. ........................................ 63
Figure 33: Spinal Displacement (CBA & Kevlar). After Ref. [13] ................................. 64
Figure 34: Sternum Acceleration (Kevlar only). After Ref. [13]. ................................... 66
Figure 35: Sternum Velocity (Kevlar only). After Ref. [13] ........................................... 67
Figure 36: Sternum Displacements (Kevlar only). After Ref. [13]. ................................ 67
Figure 37: Spinal Acceleration (Kevlar only). After Ref. [13]. ....................................... 68
x
Figure 38: Spinal Velocity (Kevlar only). After Ref. [13]. ............................................. 68
Figure 39: Spinal Displacement (Kevlar only). After Ref. [13]. ..................................... 69
Figure 40: Sternum Acceleration (Kevlar and CBA plate without muscle). After Ref.
[13]. ················································································································· 71
Figure 41: Spinal Acceleration (Kevlar and CBA plate without muscle). After Ref. [13].
························································································································· 71
Figure 42: Sternum Acceleration (Kevlar and CBA plate without dampers). After Ref.
[13]. ················································································································· 73
Figure 43: Spinal Acceleration (Kevlar and CBA plate without dampers). After Ref.
[13]. ················································································································· 73
Figure 44: Sternum Acceleration (Kevlar and CBA plate with muscle Young's Modulus
increased by five times). After Ref. [13]. ....................................................... 75
Figure 45: Spinal Acceleration (Kevlar and CBA plate with muscle Young's Modulus
increased by five times). After Ref. [13]. ....................................................... 75
Figure 46: Sternum Acceleration (Kevlar and CBA plate with sternal cartilage Young's
Modulus increased by ten times). After Ref. [13]. ......................................... 76
Figure 4 7: Spinal Acceleration (Kevlar and CBA plate with sternal cartilage Young's
Modulus increased by ten times). After Ref. [13]. ......................................... 77
Figure 48: Sternum Acceleration (Kevlar and CBA plate with contact elements
removed). After Ref. [13]. .............................................................................. 78
Figure 49: Spinal Acceleration (Kevlar and CBA plate with contact elements removed).
After Ref. [13) .................................................................... .-............................ 79
Xl
Figure 50: Sternum Acceleration (Kevlar and CBA plate with Kevlar density increased
five times). After Ref. [13]. ............................................................................ 80
Figure 51: Spinal Acceleration (Kevlar and CBA plate with Kevlar density increased
five times). After Ref. [13]. ............................................................................ 81
Figure 52: Sternum Acceleration (Kevlar and CBA plate with CBA plate density
increased five times). After Ref. [13]. ............................................................ 81
Figure 53: Spinal Acceleration (Kevlar and CBA plate with CBA plate density increased
five times). After Ref. [13]. ............................................................................ 82
Figure 54: Sternum Acceleration (Kevlar and CBA plate with thorax dimensions
increased 25%). After Ref. [13]. ..................................................................... 83
Figure 55: Spinal Acceleration (Kevlar and CBA plate with thorax dimenstions increased
25%). After Ref. [13] ...................................................................................... 84
Figure 56: Models of Viscoelastic Solids. From Ref. [24] ............................................ 107
Figure 57: Model of DYNA3D Viscoelastic Solid ........................................................ 108
Xll
LIST OF TABLES
Table 1: NIJ Body Armor Classification and Testing Summary. From Ref. [12] ........... 32
Xlll
xiv
I. INTRODUCTION
Since the early twentieth century, the United States government has conducted
research in the field of protective body armor systems. Initial experiments with silk and
steel proved either to provide an inadequate level of protection or were too unwieldy as a
body armor system for soldiers. Recent advances in the field of material science have
lead to the advent of such polymers as Kevlar and Spectra, and ceramics, such as boron
carbide, that are incorporated into modem body armor systems. Although these
bulletproof vests are resistant to bullet penetrations, the forces that are imparted to the
body are still significant and potentially lethal.
The objective of research described in this thesis is to create a viable three
dimensional finite element model of the human thorax (including ribs, sternum, vertebral
column, cartilages, and major musculature) that would predict the response of a bullet
impact on a body armor system. Validation of the model was conducted by comparing
the finite element analysis results to those obtained during bullet impact analyses of body
armor systems on cadavers. Upon validation, the model was subjected to a parametric
study to determine its essential components.
With the model developed, it is possible to study the effects of different body
armor systems, different projectiles with various velocities, and the thoracic dimensions
of individuals, on the response of the thorax. This allows for realistic experimentation on
new body armor systems for the United States government without the time and cost
involved in cadaveric studies.
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2
II. BACKGROUND
A. FINITE ELEMENT ANALYSIS
1. Introduction to Finite Element Analysis
Finite Element Analysis (FEA) or the Finite Element Method (FEM) has
developed from its infancy in the late 1940s into the mature computational science that it
has become today. In its earliest days, the scope and the depth of problems analyzed by
this particular method were limited by the size of the matrices created. However, today,
with the enormous amounts of computing power available, areas such as structural
mechanics, heat transfer, electromagnetics, fluid flow, orthopedic implant design, and
tissue growth can all be adequately modeled and analyzed. It is becoming an integral part
of the prototyping of new designs. By allowing engineers to model a design and test it in
a computer environment, savings are realized in both time and money.
2. History of Finite Element Analysis
The ideas behind the finite element methods were first mentioned in 1943, when a
mathematician, R. Courant, first proposed the idea of taking a continuum problem,
breaking it down into triangular regions, and solving the problem in each region
individually with piecewise approximations. Unfortunately, his ideas were not
expounded upon until 1950 due to the fact that the computing power necessary to actually
implement these ideas did not present itself until almost a decade after Courant's paper.
[Ref. 1] In a ground-breaking paper published in 1956, Turner, Clough, Martin, and
Topp established the original method, developed out of a problem originating in the
3
1930s. A structural engineer had been presented with the issue of how best to solve for
the component stresses of a loaded truss. The issue was relatively straightforward and
followed simple statics. Yet, this was only for the case of a finite number of
interconnections. The question arose about how to deal with the problem if a plate
replaced the truss. In this instance, an infinite number of interconnection points would be
present. Hrenikoff proposed a solution by dividing the plate into elements or structural
sections connected at a finite number of nodes. This allowed the problem to be resolved
by conventional means and it planted the seeds for the finite element method. In fact, this
idea was further developed and a solution presented in the paper by Turner, Clough,
Martin, and Topp. It was in an extension of this work by Clough in 1960 where the name
'finite element method' first appeared.
Consequent developments in the field of finite element analysis have resulted in
continued refinements to the original method. Additionally, the field has grown to
encompass various disciplines such as thermodynamics, electromagnetics, and
biomechanics. The advent and continued advances in computers have also significantly
affected the implementation of finite element analysis. Today, numerous computer
programs have been developed to help make the different steps of the finite element
method easier and more automated. Computer programs can now take information from
computer-aided design (CAD) and computer-aided manufacturing (CAM) programs and
use this as a basis for the finite element model, saving time and reducing errors.
4
3. How the Method Works
In a continuum problem, the variables to be analyzed possess an infinite number
of values because each is a function of a particular point in that region or body.
Consequently, there are an infinite number of unknowns. By discretizing the region into
a collection of finite elements, the infinite number of unknowns is reduced to a finite
number. Solving for the values at nodes, or the intersection of these elements, gives a
cloud of data about the region or body. Approximation, or interpolation, functions can
then take the particular value at a specific node or series of nodes and average it across
each element. This method allows a seemingly "impossible" problem to be broken down
into a more manageable one. Now, the behavior of the field variable can be
approximately described for the entire region. Figure 1 is an example of discretizing a
given complex domain into elements.
p p
z,u -x
~~ ~L~~ ~ N
1. I~ (a) (b)
Figure 1: Discretization of a Tapered Rod. From Ref. [2].
The accuracy of the data returned by the method is subject not only to the number
of nodes and elements used, but also to the particular interpolation functions that are
chosen. The determination of which functions to use will depend on the kind of element
selected. Another important determination in the selection of the interpolation function is
5
to ensure that the data will be continuous across element boundaries. Figure 2
demonstrates the potential discretization of a complex geometry and the resultant forces
applied after creation of the finite element model.
Figure 2: Discretization of a Plate Member. From Ref. [2].
Finite element analysis relies on several different approaches to solving a given
problem. These include the direct approach, the variational method, and the weighted
residuals method. The direct approach is a relatively simple method, based on the direct
stiffness method of structural analysis, with the limitation that it can only be used on
elementary problems. By understanding the points at which various beams intersect and
the angle of their intersection, their transmission of forces from one to another can be
calculated. By breaking down the complex structures into simpler elements, the "force
deflection," or stiffness, characteristics of that particular element can be determined.
Matrices can be constructed that represent the stiffness of each individual member. By
combining these matrices, the stiffness for the entire structure can be determined. This
method of calculating the effects of loads on framed structures became known as the
direct stiffness method and resulted in the first approach to solutions in finite element
analysis. [Ref. 3]
6
The variational approach to representing element properties relies on the calculus
of variations and involves extremizing a functional. These functionals are dependent on
the type of problem being studied. For example, in solid mechanics, the functional is the
stationary potential energy. This method allows finite element analysis to extend beyond
the limit of simple elements in structural mechanics and become incorporated into other
fields. It also allows for the use of sophisticated element shapes, unlike the simple shapes
required by the direct approach. [Ref. 4]
The most versatile of the approaches is the weighted residuals method. It can be
used in cases where no functional can be defined, such as in nonstructural element fields
like heat transfer and fluid mechanics. This method relies on a set of established
governing equations defined for the problem, without requiring a variational function.
This allows the finite element method to be utilized in different scientific fields than
those opened up by either the direct or variational approaches. [Ref. 4]
The basic steps taken to perform a finite element analysis are the same regardless
of the approach being used. The first step is to develop the model for the analysis. This
includes creating the geometric representation of the object, defining the domain and
boundary conditions, defining material properties for the model, and apply the loads to be
studied. Included in this step are any model idealizations that can be specified to simplify
the model. This may include modeling only one side of a symmetrical object under a
symmetrical load or renumbering nodes to minimize bandwidth of the required matrices.
Due to the computer- and time-intensive nature of finite element analysis, any
simplifications can significantly reduce computation costs.
7
The next step in the finite element method is to discretize the model and domain
into finite elements and ensure that they are properly connected. This is a step of
compromise. As the model is being discretized, the size, shape, and number of elements
created becomes important. Figures 3, 4, and 5 show examples of elements that should
and should not be used in the discretization. These parameters will determine the
accuracy that is returned. If the elements created are too large and do not adequately
model the region or body being analyzed, the data returned will be inaccurate. However,
if the elements created are too small, the time and number of calculations required to
arrive at a solution will be too large.
~~•-a;:y---~ O:>>Pi
HillltlY~
Figure 3: Elements having Shape Distortions that Tend to Promote Poor Results. From Ref. [2].
" 3
18 20
5
Figure 4: Eight Noded Brick Element. Figure 5: Twenty-Noded Brick Element. From Ref. [2]. From Ref. [5].
8
The next step is to perform the analysis itself. This is the application of one of the
various methods, direct, variational, or weighted residuals, to the finite element model.
The final step is to verify the accuracy of the results and conduct any post
processing. The accuracy can be checked by several methods, including refining the
model to check for convergence, and parametric studies. Post-processing, on the other
hand, allows for accurate and complete documentation of the analysis results. This
includes creating a graphical representation of the problem and the results so that the data
are easily accessed and pertinent information can be easily extracted.
4. Range of Applications
There are three basic categories into which the applications of the finite element
method fall. The first is the time-independent, or static analysis, problem. This contains
the majority of the current uses for finite element analysis. The solutions are all created
under steady-state conditions.
The second category into which finite element analysis applications fall is the
eigenvalue problem. These problems are an investigation of the long-term state of a
system. In addition, this type of problem can determine the natural frequencies and
modes of vibrations in areas such as solid and fluid mechanics. These types of
applications also include such as the stability of structures and the stability of laminar
flows.
The final category is time-dependent or propagation problems. These problems
must also consider the variable of time and its effect on a system. Those studying
9
continuum mechanics are most interested in this area of application. It is these dynamic
problems that were the focus of this study.
The finite element method is being incorporated into almost every field of
engineering. Whereas the original users of the method were mostly civil, mechanical, or
aerospace engineers, the finite element method has spread to various disciplines such as
heat transfer, fluid mechanics, electromagnetics, and biomechanics. This widespread use
illustrates the power and opportunities in the finite element method.
B. PROPERTIES OF BONE
The skeleton consists of 200 bones of various shapes and sizes as depicted in
Figure 6 below. Bone consists primarily of calcium and phosphorous. Included in the
chemical composition are traces of magnesium, fluorine, chlorine, and iron. Bones, a
living tissue, are grown by the expansion of an epiphyseal plate. As the plate expands,
the cartilaginous growth plate beneath it is subsequently calcified and turned into
compact bone. For flat bones, it is the calcification of membranous tissues that leads to
the construction of the bone. Surrounding the bone, except at the points of articulation, is
a thin layer called the periosteum. The interior layer of the periosteum contains cells that
provide enlargement and remodeling of a growing long bone. After the bone has
matured, the inner layer becomes primarily a network of capillary blood vessels and the
outer layer becomes fibrous. However, if subject to injury, the inner layer of the
periosteum can once again become osteogenic. [Refs. 6 & 7]
10
Corpus
M.ta.carpus
Phalans•s
Ribs
Rodiua
Ulna Ilium Sacrum
~=IJ~~:~~:x ~-l!T~c--hchium
Tarsus Metatar1ua Phalanges
Figure 6: Human Skeleton. From Ref. [7].
Bones can be classified in four broad categories. These are long, short, flat, and
irregular. Long bones, as illustrated in Figure 7 below, are the primary members of the
limbs, where they are used to support the weight of the trunk and to provide the
foundation for locomotion. These bones consist of a diaphysis and two epiphyses. The
diaphysis is a tube of compact bone with the greatest thickness at the middle of the bone.
Inside the tube is a thin layer of spongy tissue ( cancellous bone) with a medullary canal
running the length of the bone. The medullary canal is the location of the bone marrow.
The extremities consist of primarily cancellous bone with a thin shell of compact bone.
11
In addition, the epiphyses have a large surface area to provide room for muscle
attachments and articulations with neighboring bones .
.;.mll~~-~-Epiphysis f'liil~~~~ . ....,~-Grolilltn plate
Articular cartilage
Figure 7: Long Bone. From Ref. [6].
The short bones provide strength and compactness while allowing for small
movements. They are primarily found in the hands and feet (carpus and tarsus). Except
for a thin shell of compact bone at the surface, they consist primarily of spongy bone.
The ribs, sternum, and bones of the cranium and face characterize the flat bones.
Their primary purpose is for broad muscle attachments or protection. These bones
consist of two thin layers of compact bone with spongy bone in the interior.
12
The irregular bones are those that do not fit into any of the previous categories.
However, they do share the same general composition of compact bone on the exterior
and spongy bone on the interior.
Bone is not a homogenous material. It is a composite of Haversian units, also
known as osteons. The center of each osteon is an artery or a vein, called the Haversian
canal, with transverse Volkmann's canals connecting adjacent units. The inorganic
materials, such as calcium and phosphorous in a form called hydroxyapatite, make up
two-thirds of the weight of bone. The remaining weight is primarily in the form of
organic collagen fibers. These fibers can be either in parallel packages called lamellae or
in a tangled web, dependent upon the type of bone. Within each osteon, the lamellae are
arranged in approximately six to eight concentric circles about the Haversian canal.
However, in the interstitial space between Haversian units, the lamellae are primarily
parallel to the surface of the bone. Lacunae are small cavities equally spaced between
lamellae. These cavities radiate canaliculi and connect with the Haversian canals. This
network penetrates the bone matrix allowing for the transmittal of nutrients and removal
of wastes from the cells of the bone. A cross-section of a long bone is depicted in figures
8 and 9 below.
13
Figure 8: Cross-section of Compact Bone. From Ref. [7].
The primary cells of bone are the osteoblasts, osteoclasts, and osteocytes. The
osteoblasts are found in a layer adjacent to the periosteum. They are primarily
responsible for the formation of bone tissue. Osteoclasts are located at sites of bone
reabsorption and are primarily responsible with dissolving bone for remodeling.
Osteocytes are the mature, permanent bone cells of osseous tissue and differentiate from
the osteoblasts.
14
Fib,.ou.., lc:r.:yo:r ot f>"'':'io&i:au."T'\.
o .. t .. og12ni<: lcr.y .. r of pario-.teuin.
¥1'~~~- end.o<>tcoa.t li.ni"':S or
f)..;;;~~- hc:r.YctPSia.'11. ea.nQ.\.
.. !
Figure 9: Basic Structure of Compact Bone. Original from Ham (1969). From Ref. [6].
The mechanical properties of bone are dependent upon its structure as a
composite of minerals and collagen. However, bone's strength is higher than either of its
constituent parts. This is due to the softer component (collagen) preventing the stiffer
material (hydroxyapatite) from brittle cracking and the stiff component preventing the
softer one from yielding.
Stress-strain curves have been obtained from placing human femurs under tension
loads. As such, it has been determined that dry bone is brittle and fails at a strain of
0.4%. On the other hand, wet bone fails at 1.2% strain. Due to the initial linear nature of
the stress-strain curves, it is possible to determine a Young's modulus for bone. It is
important to note that the Young's modulus depends upon the load type and rate applied
to the bone. Due to its anisotropic nature, the Young's modulus for a femur under
15
tension is approximately three times higher than that of a femur under compression.
Stress-strain curves, such as those depicted below in Figure 10, can also be utilized to
determine the ultimate tensile strength, the yield point, and the strain energy of bone. It
is important to note that these tests were performed for the femur, which consists of both
cortical and cancellous bone. (Cancellous bone tends to fail at 75% strain, whereas
cortical fails at 2% strain.) [Ref. 6]
MP a Human femur (after Evans 1969)
80
70
60
"' 50 <I)
!!? Vi 40
30
20
10
0 0 0.002 0.004 0 0.002 0.004 0.006 0.008 O.OIO 0.012
Strain
Figure 10: Stress-Strain Curves of Human Femur. Original From Evans (1969). From Ref. [6].
Bone exhibits both brittle and ductile behaviors. Additionally, due to its
anisotropy, the behavior of bone subjected to applied forces will vary dependent upon the
mechanical properties, the geometry, the loading modes, the loading rate, and the
frequency of load application. Other important considerations in the calculation of the
mechanical properties of bone are the sex and age of the subject, the location of the bone,
the orientation of the load, the strain rate, and whether the bone is wet or dry. Due to the
16
uniqueness of each of these parameters for an individual, it is impossible to develop an
average value for humans in general.
C. PROPERTIES OF CARTILAGE
Cartilage is found in various sites around the body, including the ears, nostrils,
joints, and in the thorax. All three types of cartilage share the same basic elements: cells,
intercellular matrix, and system of fibers. The varieties include hyaline cartilage,
fibrocartilage, or fibroelastic cartilage, dependent upon the matrix in which the cartilage
cells ( chondrocytes) are imbedded. Cartilage can also be classified according to its
position in the body. In this case, cartilage can be articular, interarticular, costal, or
membraniform. [Ref. 8]
Hyaline cartilage covers the ends of bones within joints, acting as a shock buffer
and providing smooth surfaces for articulation. Except at points of articulation, it is
covered by a membrane that provides the chondrocytes with nutritive fluids. Articular,
costal, and temporary cartilage are all of the hyaline variety. The only difference
between them is the size and shape of the chondrocytes and the exact arrangement of the
matrix. Articular cartilage has a finely granular matrix. It grows in response to the
location of the largest stress. As such, it will be thickest at a tubercle or other protrusion
that receives a majority of the force on a joint. Costa! cartilage has large cells and fibrous
striations in the matrix. For all three types of cartilage, calcification can occur. For the
temporary cartilage, it is this calcification that allows for the cartilaginous skeleton of the
human fetus to develop into the bony skeleton. [Ref. 7]
17
Fibrocartilage is found in the intervertebral discs, the semilunar cartilages of the
knee joint, and the cartilage of the symphis pubis. It consists of a mixture of white
fibrous tissue and cartilaginous tissue in various proportions. The fibrous tissue allows
for flexibility and toughness, whereas the cartilaginous tissue provides elasticity. In the
case of the intervertebral disc, this allows for shock absorption while still maintaining
flexibility in the spine. The fibrocartilage can be of several varieties, including
interarticular, connecting, circumferential, or stratiform, depending upon appearance and
location. [Ref. 7]
The least pervasive type of cartilage is fibroelastic cartilage. It is found in certain
small cartilages of the larynx, the epiglottis, and the ear. Similar to the other types of
cartilage, it is differentiated by the network of tangled yellow elastic fibers that permeate
its matrix. [Ref. 7]
Cartilage is a rather porous material, allowing for the movement of fluids in and
out of the tissue. The physical structure responsible for this fluid absorption and
di~charge is chains of proteoglycans, large protein-polysaccharide molecules, which
create the intracellular matrix of cartilage. Additionally, friction between these chains is
responsible for the creep and stress relaxation that characterize the viscoelastic properties
of cartilage. [Ref. 9] For example, upon indentation, cartilage will have an immediate
recovery followed by a time-dependent one. This flexibility is what allows the thorax to
change shape as the lung inhale and exhale. Additionally, this property allows cartilage
to have an extremely low coefficient of friction while still maintaining a long lifetime. It
is thought that this occurs due to the presence of the fluids in the extracellular matrix. As
18
the fluid is squeezed out, the coefficient of friction increases. Thus, joints, such as the
synovial joints, are so effective because the time required for the fluids to be squeezed
through the matrix is long and once the load is removed, the compressed cartilage
rebounds quickly and reabsorbs the synovial fluid. This creates a unique system that is
adapted for both shock absorption and lubrication of points of articulation. [Ref. 6]
D. ANATOMY OF THORAX
The human thorax consists of an osteo-cartilaginous cage to protect the primary
organs of respiration and circulation. Its posterior surface consists of the twelve thoracic
vertebrae and the sternum; the costal cartilages form the anterior surface. The ribs form
the lateral surfaces. The upper boundary of the thorax is formed by the first thoracic
vertebra, the superior of the sternum, and the first rib pair. The lower boundary of the
thorax is the diaphragm which connects the twelfth thoracic vertebra, the twelfth rib pair,
and the subcostal angle formed by the cartilage of the seventh, eighth, ninth, tenth, and
eleventh rib pairs. A posterior view of the thorax, illustrating the sternum and costal
cartilages, is depicted in Figure 11 below. [Ref. 8]
The differences between the male and female thorax are minor. On the female,
the general volume is smaller than that of a male, the sternum is shorter, the superior
portion of the sternum is generally in line with the lower portion of the third thoracic
vertebra rather than the lower portion of the second thoracic vertebra in males, and the
upper ribs are more flexible. [Ref. 8]
19
$UPRASTl!RHAL NOTCH
'
Figure 11: Sternum and Costal Cartilages. From Ref. [7].
1. Spine
In general, the spine consists of 34 vertebrae, 23 discs, and their connecting
ligaments. The function of the spine is to form a strong support structure for the head and
trunk, to protect the spinal cord, and to provide rigidity for the suspension of the limbs.
There are three major regions: cervical vertebrae (7), thoracic vertebrae (12), and lumbar
vertebrae (5). The additional vertebrae are included as either sacral vertebrae (5), which
are fused together to form the sacrum, or coccygeal vertebrae (5), which are fused
together to form the coccyx. These regions, in tum, provide a metho<;l for naming each
vertebra. The vertebrae in each region are labeled with a C, a T, or an L, depending upon
20
whether they are in the cervical, thoracic, or lumbar region. Additionally, numbers are
assigned, with one being the most superior vertebra in that particular region. Below, in
Figures 12, 13, and 14, are illustrations of the spinal column, a lumbar vertebra, and a
cervical vertebra, respectively.
2
3
4
Cervical curve
7 Thoracic curve
Lumbar ~ve
Sacral and co ccygeal curve
5
1 to 4 or 5 coc:c:ygeal
Figure 12: Vertebral Column. From Ref. [7].
Spi~e · (spinl)us proce$$)-
Boey: ..
Inf. artic:. ·process
Figure 13: Lumbar Vertebra. From Ref. [7].
Spine
A
Bodv Figure 14: Cervical Vertebra. From Ref. [7].
21
A typical vertebra consists of a body and a vertebral arch, as depicted in Figure
15. The body is a thick disclike mass of cancellous bone with a thin covering of compact
bone, situated anteriorly to the spinal cord. The body is convex horizontally in front and
concave behind to form one side of the canal for the spinal cord. The vertebral bodies are
stacked one on top of another, with intervening discs of cartilage, to form the vertebral
column, as in Figure 16. The vertebral arch is located posteriorly of the body and closes
off a space between the body and the arch called the vertebral foramen. The vertical
alignment of this foramen creates the spinal canal and is the location of the spinal cord.
The vertebral arch consists of two pedicles, two laminae, a spinous process, two
transverse processes and four articular processes to interact with the neighboring
vertebrae. The pedicles are two angled protrusions of bone sprouting from the body in a
posterior direction. The laminae extend from the pedicles and meet in the midline,
posterior from the center of the vertebral body. At the point of confluence, the spinous
process is born and points backwards and downwards. The spinous process articulates
with the spinous process of the vertebra beneath it. This adds additional support to the
vertebral column. The transverse processes protrude laterally and posteriorly from the
junction of the lamina and the pedicle. The articular processes also point in this
direction. They are found in two pairs, one inferior and one superior. The superior
articular processes face backwards, whereas the inferior articular process facets face
forwards. Thus, the superior articular process of the lower vertebrae and the inferior
articular process of the upper vertebrae interact to provide lateral and medial stability to
the spine. [Ref. 8]
22
-----------------------------------------
Tran&. pro ess
Figure 15: Thoracic Vertebra (Superior and Lateral Aspects). From Ref. [7].
'--' :.. ...... •-Trons. process with facet far tubercle of rib
Facet for head of rib
Facet far tubercle of ri~
Single facet .for head of 11th rib
Figure 16: Ninth, Tenth, and Eleventh Vertebrae. From Ref. [7].
The ligaments of the spine can be divided into five sets, dependent on position.
There are those connecting the bodies of the vertebrae, the laminae, the articular
processes, the spinous processes, and those connecting the transverse processes. The
most important are the interspinous ligament and the supraspinous ligament. The
interspinous ligament is thin and membranous and extends from the root to the summit of
the spinous processes between each vertebra. The supraspinous ligament is a strong cord
23
connecting the spinous processes from the seventh cervical vertebra to the sacrum. [Ref.
8]
2. Ribs
The ribs are 24 bowed bones in 12 pairs. Articulating with the thoracic vertebrae
posteriorly and the sternum anteriorly, they form the framework for the thorax. They are
numbered in ascending order with the most superior rib as one. This numbering
corresponds to the thoracic vertebra that each rib pair articulates with as well. Ribs one
through seven, as represented in Figure 17 below, are called the true ribs due to their
direct connection to the sternum through costal cartilage. Ribs eight through twelve are
false ribs. Ribs eight, nine, and ten share a common connection to the sternum through
the subcostal angle, whereas ribs eleven and twelve are floating ribs with no connection
to the sternum at all. The direction of the ribs varies as well, with the upper ones less
oblique than the lower. The ribs increase in length from the first to the seventh, then they
begin to decrease through the twelfth. The largest breadth of the rib is at the attachment
point of the sternum. [Refs. 7 & 8]
Each rib has two extremities: the posterior (vertebral) and anterior (sternal). The
connecting section is referred to as the shaft or body. The posterior section includes the
head, a neck, and tuberosity. The head contains two facets for articulation with the
articular surface created between the body of two adjacent vertebrae. Additionally, the
head is attached to the intervertebral disc through a short ligament between the articular
surfaces. The neck is the intervening region between the head and the tuberosity. It has a
flattened portion for attachment of various ligaments. The articular tuberosity interacts
24
with the transverse process of the lower vertebrae. The shaft is thin, flat and is bowed
and twisted as it proceeds from the vertebral to sternal extremity. Finally, the sharp bend
both superiorly and anteriorly in the shaft is referred to as the angle. The anterior end of
the rib is flattened and porous allowing for attachment via collagen anchors of the costal
cartilage. [Ref. 8]
A
Facets on head.
' c ,_/
Junction with costal cartilage of sternum
Figure 17: (a) Fifth Rib, Inferior Aspect; (b) Fifth Rib, Posterior Aspect; (c) First Rib. From Ref. [7].
The ribs are not uniform, and the first, second, tenth, eleventh, and twelfth exhibit
interesting peculiarities. The first rib is the shortest and the most curved. The second
25
also exhibits sharp curves but is much longer than the first. The tenth rib only has one
articular facet on its head. The eleventh and twelfth each have only one articular facet
and they do not have a neck or tuberosity. Finally, the twelfth rib does not demonstrate
an angle, whereas the angle in the eleventh rib is slight.
3. Sternum
The sternum is a flat, elongated bone situated in the median of the front of the
chest. It consists of three individual portions. The upper segment is referred to as the
manubrium, the middle section is called the gladiolus, and the lower, pointed section is
called the xiphoid process. The sternum is slightly convex in front and concave in back.
See Figure 18. The manubrium is of a triangular shape with lateral depressions for the
articulation of the first costal cartilage. A notch on the inferior surface of the manubrium
and a similar notch on the superior edge of the gladiolus create a depression for the
articulation of the second costal cartilage. The gladiolus is relatively long and narrow.
Its anterior surface is essentially flat, whereas the posterior surface is slightly concave.
The lateral surface is marked with both inferior and superior notches for articulation with
the seventh and second rib pairs, respectively. Included along its lateral edge are
depressions for the costal cartilage of the third, fourth, fifth, and sixth rib pairs as well.
The xiphoid process, also called the ensiform appendix, is the smallest of the three. It
articulates with the gladiolus on its superior edge with depressions for the articulation of
the seventh rib pair. [Refs. 7 & 8]
26
Figure 18: Posterior Aspect of the Sternum. From Ref. [8].
4. Costal Cartilage
The costal cartilages are bars of hyaline cartilage that extend the ribs forward to
the connection with the sternum. Due to the mechanical properties of cartilage, this
articulation significantly affects the flexibility of the thorax and its ability to absorb loads.
The first seven pairs of costal cartilage directly attach ribs one through seven to the
sternum. Costa! cartilages eight, nine, and ten directly attach to the costal cartilage of the
rib pair directly superior to it. There are also portions of costal cartilage attached to the
last two rib pairs, however, these do not attach to the sternum and merely cover the
anterior extremity of the bone. The posterior extremity of the costal cartilage is
continuous with the osseous tissue of the rib from which it arose. The superior
extremities of the second through seventh costal cartilages end in small, smooth, oval
shaped facets to articulate with the corresponding depression in the sternum. Contrarily,
27
the superior costal cartilage of the first rib pair is continuous with the osseous tissue of
the sternum. [Ref. 6]
E. BODY ARMOR
1. A History of Body Armor
The history of body armor is as varied as the types of weaponry employed over
the years. Initially, humans utilized animal skins for protective clothing and wood for
shields. With the advancement of metallurgy in the Middle Ages, metal shields were
developed and, consequently, the use of metal in suits of armor became widespread.
However, the introduction of firearms around 1500 led to the obsolescence of these body
armor systems. [Refs. 10 & 11]
The development of soft armor for protection is credited to the medieval
Japanese. Creating a garment made from silk, it gave their warriors minimal protection
for use in combat. However, the introduction of soft armor into the United States did not
occur until the late 19th century. Relying on the same materials as the medieval Japanese
had used, the military attempted the manufacture of soft armor from silk. However, the
material was shown to be ineffective against the new higher velocity bullets(> 600 ft/sec)
used at that time. Additionally, the cost per garment was prohibitive to widespread use.
World War I precipitated an increase in research into body armor to protect
against shell fragments, but the materials were not available to create a vest with the
correct protection for a reasonable weight. [Ref. 1 O]
28
The outbreak of World War II led to renewed interest in body armor. Several
variations were tried, utilizing materials such as overlapping plates of steel, aluminum, or
bonded fiberglass incorporated into a vest of ballistic nylon. These vests were
lightweight and flexible while providing protection from shell fragments. However, the
"flak jackets" did not provide adequate protection against rifle and pistol threats.
In the 1960' s, the development of new fibers made the modem generation of
bullet proof vest possible. Additionally, research in ceramics and composites, such as
boron carbide, led to the creation of vests reliant upon a mesh of ballistic fibers while
incorporating composite layers of steel or hard ceramics into their design. These vests
have demonstrated their effectiveness in stopping even armor-piercing bullets. [Ref. 1 O]
2. Armor Classification
The National Institutes of Justice have developed a standard (NIJ Standard-
0101.03) to establish six formal armor classification types, as well as a seventh special
type. A table of the requirements is summarized below as Table 1. These are as follows:
Type I (.22 LR; .38 Special). For protection against .22 Long Rifle High-Velocity
lead bullets, with nominal masses of2.6 g (40 gr), impacting at a velocity of 320 mis
(1,050 ft/s) or less, and against .38 Special roundnose lead bullets, with nominal masses
of 10.2 g (158 gr), impacting at a velocity of259 mis (850 ft/s) or less. It also provides
protection against most other .25 and .32 caliber handgun rounds. [Ref. 12]
Type II-A (Lower Velocity .357 Magnum; 9mm). This armor protects against
.357 Magnum jacketed soft-point bullets, with nominal masses of 10.2 g (158 gr),
impacting at a velocity of 381 mis (1,250 ft/s) or less, and against 9mm full-metal
29
jacketed bullets, with nominal masses of 8.0 g (124 gr), impacting at a velocity of 332
mis (1,090 ft/s) or less. It also provides protection against such threats as .45 Auto, .38
Special +P, and some other factory loads in caliber .357 Magnum and 9mm, as well as
the Type I threats. [Ref. 12]
Type II (Higher Velocity .357 Magnum; 9mm). This armor protects against .357
Magnum jacketed soft-point bullets, with nominal masses of 10.2 g (158 gr), impacting at
a velocity of 425 mis (1,395 ft/s) or less, and against 9mm full-jacketed bullets, with
nominal velocities of 358 mis (1,175 ft/s). It also protects against most other factory loads
in caliber .357 Magnum and 9mm, as well as the Type I and II-A threats. [Ref. 12]
Type III-A (.44 Magnum; Submachine Gun 9mm). This armor protects against
.44 Magnum, lead semi-wadcutter bullets with gas checks, nominal masses of 15.55 g
(240 gr), impacting at a velocity of 426 mis (1,400 ft/s) or less, and against 9mm full
metal jacketed bullets, with nominal masses of 8.0 g (124 gr), impacting at a velocity of
426 mis (1,400 ft/s) or less. It also provides protection against most handgun threats, as
well as the Type I, II-A, and II threats. [Ref. 12]
Type III (high-powered rifle). This armor, normally of hard or semirigid
construction, protects against 7.62mm full-metal jacketed bullets (U.S. military
designation M80), with nominal masses of9.7 g (150 gr), impacting at a velocity of 838
mis (2,750 ft/s) or less. It also provides protection against threats such as 223 Remington
(5.56mm FMJ), 30 carbine FMJ, and 12-gauge rifled slug, as well as the Type I through
III-A threats. [Ref. 12]
30
Type IV (armor-piercing rifle). This armor protects against .30-06 caliber armor
piercing bullets (U.S. military designation APM2), with nominal masses of 10.8 g (166
gr) impacting at a velocity of 868 mis (2,850 ft/s) or less. It also provides at least single
hit protection against the Type I through III threats. [Ref. 12]
Type IV body armor provides the highest level of protection currently available.
Designed to stop "armor-piercing" bullets, this armor often uses ceramic materials. Due
to the brittle nature of these materials, they may only provide protection for a single shot.
[Ref. 12]
Special type. This type is set aside for a consumer who has special requirements
for body armor. As such, the consumer can specify the type of projectile to be used and
the minimum impact velocities. It is put upon the manufacturer to construct the armor to
resist these impacts. [Ref. 12]
31
Test variablea Pcdnmumce requirements
R!lqllired Required fair :bi&s fairhita
MiDimam per armor per lll'DIOl'
Nomiml required part at O" Mu:imma part lt.30° Amar Teat Tat bullet bullet angle of depth of SDJie of type Raund Dml.milii.oa mua velocity incidmce defamudion incidence
1 38 Spcc:ial lo.2J 2S9m/• 4 44mm. 2 RNLmd 158gr (850 ft/a) (l.73 in)
2 22LRHV 2.ti g 32Dm/1 4 44 2 i.e.d 40 gr (1050 ft/a) (l.73 in)
1 357Magimm 10.2g 3Blm/1 4 44mm. 2
ll·A JSP 1S8gr (12SO ft/a) (L73in)
2. 9mm. 8.0& 332m/I 4 44mm 2 FM1 124 JI" (1090 ft.ls) (1.73m)
1 3S7Mapum. 10.2 425m/a 4 "4mm 2 n ISP 1S8gr (139S ft/a) (L73iD)
2 9mm S.Og: 3SBaJa 4 #ma 2 FMJ 124sr (1175ft./1) (1.73m)
1 44?Upmn l.S.SS I 426mJ• 4 414 mm. 2 LadSWCGll 2AO Jl' (1400ff/1) (L73 in)
m-A Chr:d:cd
2 9mm. 8.01 -426m/1 4 #mm 2 FMT 124gr {1400 ftfl) (1.73 ill)
7.62mm 9.71 S38m/1 6 44mm 0 m (308 Wlnehcstet) JJO sr (27Sl'Jftf1) (1.73 in)
FMJ
»--06 10.8 g 1168 m/a 44mm 0 IV
~ 166gr (28SOft/1) (1.73 in)
Spccill • 44mm .. ~I (1.73 In) (sec: KC. 2.2. 7)" . ,_
• Tlicx itaDI =- be specified by die user. All or rhe item muat be spceificd.
Notm: Amor pau covering the IOrlO 6oat ud 1ono b.U, with or withaut aide coverage, lhall each be impacted with the indicafed 'llumber of fair hitl. Ar.mer pub covering the pom 11114 coccys lhall each be imp9ctc4 WI.th thnie Wr Jii11at0" Uglc: af mmcuc:iG. Tb.c ~mwioSl due to die mt fair bit uall be meaun6 to dctenninl: comptimce.. No fair hit bullet or one implcting at a velocity lawet tlmn the mini.mum. required bullet velocity shall pcad:Wc the lll1DOr.
Abbrcviatiom: .AP - Amor l'ien:iDg FM:r - Full Metal Jacteicd !SP - IachtmSoft Paint
LRHV - Lmlg Rmc High Velocity , RN - Round NOie
SWC - Semi-Wadcotter
Table 1: NIJ Body Armor Classification and Testing Summary. From Ref. [12].
32
3. Classification Requirements:
Types I, II-A, II, and III-A armor are required to prevent penetration from the
impact of six bullets at specified velocities and locations for two types of ammunition,
including two shots at a 30° angle. Additionally, a maximum of 44mm of deformation to
a clay model is allowed. This is to judge the effectiveness of the vest in blunt trauma.
Finally, the armor must meet these requirements while both dry and wet. [Ref. 10]
Type III armor requirements are identical to those above, except that only one
type of ammunition is specified, and all six test rounds are fired perpendicular to the
surface of the armor. [Ref. 10]
Type IV armor is required to resist penetration from only a single type of
ammunition (armor piercing) and is only required to prevent penetration from a single
perpendicular impact. This last requirement is due to the inclusion of ceramic plates in
many type IV body armor systems and the brittle nature of the ceramic material
guaranteeing protection for only a single shot. [Ref. 1 OJ
a. Wet Testing
Due to the lubricating action of water, it has been shown that the ballistic
efficiency of a fabric can be reduced by 20% when wet. As such, the NU has devised a
test to insure that fabrics will still meet the minimum requirements for their type even
when saturated from perspiration, rain, or other form of precipitation. Laboratory tests
conducted by the U.S. Army Natick R&D Command, using a mannequin that simulates
human perspiration, verified that vests will absorb perspiration in significant amounts. A
33
series of tests was also conducted by a research team from the Department of Justice, in
which officers wearing untreated vests were subjected to strenuous exercise on a hot
humid day. The amount of perspiration in the vests corresponded to the Natick
experiments. Tests conducted on these vests verified the significant reduction in the
efficiency due to water. In view of this, the NIJ standard requires that a vest continue to
provide the rated level of ballistic protection when wet. Due to these requirements,
manufacturers use materials that are inherently waterproof, treat the fibers with a water
repellant, cover the fabrics with a water repellant material, or any combination thereof.
[Ref. 10]
b. Angle Shots
All Type I through Type III-A body armors are required to resist the
penetration of bullets striking at an angle to the surface, because the probability of being
hit exactly perpendicular to the surface is low. Certain fabrics are less efficient
ballistically by as much as 20 percent when a bullet strikes at an angle. Armor must
provide the rated level of protection regardless of the angle of impact. [Ref. 12]
c. Performance Testing
The NIJ has established its own standard on conducting performance tests
of bulletproof vests. The following graphic, Figure 19, shows the test setup for ballistic
testing of police body armor. The armor to be tested is placed on a clay mold. The
consistency of this mold is controlled to ensure accurate deformation data. The
chronograph measures the bullet velocity to ensure that each test round is within the
range required by the standard. Additionally, the location of each impact is prescribed.
34
This is done to simulate real-world conditions in which impacts are not on the center of
the sternum. Figure 20 shows the impact positions prescribed by the NIJ. It is vital that
the vest provides the protection required by its type, regardless of impact location.
A - 5 m j::.r tyl'.le I, II-A. II, and Ill-A armors; 15 m for lype Ill and rl Hmors.
6 - 2 m n•inimum C - Appro~imately 0.5 to ts m
Figure 19: Range Set-up for Test Firings. From Ref. [12].
._'II' 1 / \
/ \ .f \
; ' / \
/ ' / \ ~ '
I ,,.6 '\ +41'/ • ''(5
/ ' / \ .f '
#2 / \ ,,.3 "'-----------------------·
All shots at least 7.6 cm (3 inl from any edge and at least 5 cm (2 in) from another shot
Figure 20: Impact Locations for NIJ Testing. From Ref. [12].
35
The armor is tested both while dry and after being sprayed with a
measured quantity of water for 3 minutes on each side before being mounted on the clay.
Both the front and back of the armor are tested, and tests are conducted on groin and
coccyx protection panels, if present. [Ref. 1 O]
Although in use by the NIJ, judgement of the efficacy of a body armor
material based on clay deformation testing alone has been called into question. Based on
test-firings done on goats with bulletproof vests, early tests oflow-velocity rounds led to
the development of the clay-based model test protocol. The correlation between clay
deformation and trauma to the goats has been good for low-velocity projectiles.
However, experiments have not been conducted to assess the validity of these clay model
tests for high-velocity or large-caliber projectiles. As a result, DeMaio, et al, at the
Armed Forces Institute of Pathology, have tested the effects of high-velocity bullets on
cadavers wearing a protective vest. As expected, none of the projectiles were able to
penetrate the vest; however, the force imparted to the thorax created internal injuries that,
in their assessment, would have been lethal. As such, this study has called into question
the validity of clay model deformation testing for type determination as the sole
determinant of protection for an individual. [Ref. 13]
d. V50 Testing
Another comparative testing method has emerged from use by the
military. The VSO ballistic limit testing is a statistical test to evaluate hard armor of
homogenous construction used to protect vehicles. It has been incorporated by many
manufacturers into the design and assessment stage of their body armor systems. V50
36
testing as used by body armor manufacturers experimentally identifies a velocity at which
a specific projectile has a 50-percent chance of penetrating the armor being tested. In this
form of testing, the armor is mounted and bullets are fired to determine the velocities at
which the bullets do and do not penetrate the armor. A sufficient number of bullets are
fired at various velocities to obtain groups of five nonpenetrating bullets and five
penetrating bullets, with a velocity range of no more than 38 mis (125 ft/s) between the
lowest velocity nonpenetrating bullet and the highest velocity penetrating bullet. The
V50 ballistic limit is calculated as the average velocity of the 10 bullets. [Ref. 14]
V50 ballistic limit testing allows manufacturers to evaluate various
designs against one another to optimize their design for a specific type of body armor.
V50 ballistic limit testing is a useful and informative statistical tool for evaluating certain
characteristics of armor. In addition to being helpful during the design phase of armor
development, it may also have the potential for being a valuable tool in evaluating
armor's degradation over time. However, it does not evaluate the level of protection
afforded against blunt trauma, nor is a uniform standard for V50 ballistic limit testing
used by all manufacturers. Therefore, it is not suited for use in a performance standard.
[Ref. 14]
4. Body Armor Construction
By deforming a bullet upon impact, the soft armor in a protective vest dissipates
the kinetic energy of the bullet into the multiple layers of the vest. The fibers absorb and
disperse, through strain, the impulse momentum that is transmitted to the vest from the
bullet, causing the bullet to deform or "mushroom." The vest must provide a resistive
37
force, F, for a time, ~t, so as to reduce the momentum of the bullet to zero according to
Fflt = m!:iv =impulse. The vest is designed to make ~t as large as possible and to
spread the force over as large an area as possible. Each successive layer of material in
the vest absorbs additional energy, until such time as the bullet has been stopped.
Because the fibers work together both in the individual layer and with other layers of
material in the vest, a large area of the garment becomes involved in preventing the bullet
from penetrating. This also helps in distributing the forces that can cause nonpenetrating
injuries (what is commonly referred to as "blunt trauma") to internal organs. Research by
Philip Cunniff at the U.S. Army Natick Research site has lead to the development of a
semiempirical model of the ballistic impact performance of textile-based personnel
armor. [Ref. 15] His equations predict the residual bullet velocity after impact with a
vest layer, dependent upon the mass of the bullet, the areal density of the fabric system,
the presented area of the projectile, and the angle of incidence. Additional work has been
done by Vinson and Zukas [Ref. 16] to develop a mathematical model for the physics of
high-velocity bullet impacts to a textile fabric. Their study has created a stepwise
procedure for use a on computer to determine strains, projectile position, forces, and
decelerations as a function of time. However, their model does not incorporate the loss
of kinetic energy accompanying the deformation of the projectile.
Combining soft armor, which absorbs bullet energy, with a hard plate, such as
steel or boron carbide, it is feasible to create a vest impervious to a bullet. However,
selection of a body armor system is dependent upon the threat that will be faced. For
instance, police officers are more concerned with bullets from handguns. As such,
38
exclusively soft armor systems, which are concealable, more flexible, and, hence, more
comfortable, may be sufficient. However, for military applications, use ofrigid or semi
rigid systems will be required due to the nature of the threats faced.
a. Methods of Construction
The primary element of a body armor system is the "ballistic panel."
Created from multiple layers of a weaved ballistic fiber, these panels are inserted into a
"carrier." The carrier is essentially the harness that holds the ballistic panels in place and
is usually created of nylon or cotton. Depending upon the design, the panels may be
removable or stitched into the carrier. Additionally, pockets may be incorporated into the
carrier for insertion of the hard plates. As such, versatile bulletproof vest can be created.
The ballistic fabric is the key element of the vest. As such, its properties
are dependent upon the manufacturer and are guarded as proprietary information. Each
manufacturer incorporates different fibers with different weaves into their fabrics. The
ballistic performance of a fabric is dependent upon the method in which the fibers are
woven and the types of fibers used. Additionally, many manufacturers incorporate
nonballistic materials into the layers of the ballistic panel in order to help reduce blunt
trauma.
b. Materials Used
Due to the proprietary nature of these fibers, material properties are very
difficult to obtain. As such, the following fibers will be discussed based on the claims
made by their manufacturer.
39
Dupont has been one of the premier developers of ballistic fibers. Its
Kevlar® brand fiber, first developed in 1965, was the first material identified for use in
the modem generation of concealable body armor. Kevlar® is a manmade organic fiber,
with a combination of properties allowing for high strength with low weight, high
chemical resistance, and high cut resistance. Kevlar® is also flame resistant, does not
melt, soften, or flow, and the fiber is unaffected by immersion in water. [Ref. 1 OJ
Kevlar® 29, introduced in the early 1970s, was the first generation of
bullet-resistant fibers developed by DuPont and helped to make the production of
flexible, concealable body armor practical for the first time. In 1988, DuPont introduced
the second generation of Kevlar® fiber, known as Kevlar® 129. This fabric offered
increased ballistic protection capabilities against high-energy rounds such as the 9mm
full metal jacket. In 1995, Kevlar® Correctional™ was introduced, which provides
puncture-resistant technology to both law enforcement and correctional officers against
puncture-type threats. [Ref. 1 O]
The newest addition to the Kevlar® line is Kevlar® Protera™, which
DuPont made available in 1996. DuPont contends that the Kevlar® Protera ™ is a high
performance fabric that allows lighter weight, more flexibility, and greater ballistic
protection in a vest design due to the molecular structure of the fiber. Its tensile strength
and energy-absorbing capabilities have been increased by the development of a new
spinning process. [Ref. 1 O]
Spectra® fiber, manufactured by AlliedSignal, is an ultra-high-strength
polyethylene fiber. The fibers consist of ultra high molecular weight polyethylene
40
dissolved in a solvent, spun through a series of small orifices, and then solidified through
cooling. The fibers are then placed in two unidirectional layers, at a 90-degree angle, and
covered with a flexible resin. Finally, two thin sheets of polyethylene film are spread on
either side of the fibers and resin. The resulting fabric is the Spectra Shield™ composite.
According to AlliedSignal, the fabric is incredibly strong, lightweight, and has excellent
ballistic protection capabilities. This fabric is incorporated into a variety of styles for both
concealable and hard armor applications. The same spinning technology is used by
AlliedSignal to manufacture another type of shield composite called Gold Shield®. Gold
Shield® is manufactured using aramid fibers instead of the Spectra fiber. Gold Shield®
is currently made in three types: Gold Shield® LCR and GoldFlex®, which are used in
concealable body armor, and Gold Shield® PCR, which is used in the manufacture of
hard armor, such as plates and helmets. [Ref. 10]
F. LITERATURE SURVEY
To date, there is little existing research into the dynamics of bullet impacts to the
thorax. The predominant areas of study have been into the creation and validation of a
human thorax finite element model and into analysis of the thorax reaction to blunt
impacts in automobile collisions. A majority of the research has been concerned with
static analyses to validate human thorax finite element models. Very few studies have
examined dynamic effects on the thorax. The present research project breaks new ground
in the use of the finite element method for investigations into the biomechanical response
of the thorax to dynamic loading.
41
Research into a mathematical model of the thorax began with the studies of
Roberts and Chen in 1970. [Ref. 17] Utilizing gross geometric data and approximate
cross-sectional properties, they were able to develop an elastostatic finite element model
of the thorax. Placing the sternum of the model under various static loading cases, they
obtained reasonable data for sternal displacements, thereby validating their model. Due
to the success of their model, it has been incorporated into most of the models utilized in
later studies of the thorax. In addition, it provided the framework for the model
developed by Hughes in his work and, consequently, was incorporated into the model
developed for this study. [Ref. 18]
Andriacchi, Schultz, Belytschko, and Galante [Ref. 19] used the model developed
by Roberts and Chen in a study of the mechanics of the human skeleton. In order to
study the interactions between the rib cage and the spine, their model further refined the
existing model. In their study, they were able to examine the bending responses of the
spine, the lateral stability of the spine, and the underlying mechanisms in scoliotic
deformities. However, their analyses relied on static loading cases on the thorax and
were not very useful in the development of a valid dynamic model.
Along with the development of the geometry of a three-dimensional thorax
model, research was done into the material properties of the thorax. Due to the individual
nature of these properties, these studies compiled results for a large population. In work
by Y oganandan and Pintar, the mechanical properties of the seventh and eighth rib pairs
were determined for 30 cadavers. [Ref. 20] Utilizing three-point bending techniques on
isolated ribs, the researchers were able to determine the cross-sectional area, moment of
42
inertia, failure load, deflection, and Young's modulus. However, it is believed that
further investigation into the material pmperties of the other rib pairs as well as the costal
and articular cartilage is necessary due to the individual nature of these properties.
In the study by Hughes [Ref. 18], the data from Andriacchi, et al and
Y ongananda, et al was combined to create a viable three-dimensional model of the
thorax. The computed response due to an applied static load was studied to validate the
finite element model. In addition, a limited dynamic study of the impact of a bullet into
body armor protecting the thorax was also investigated. Numerical data were compared
to that obtained from "live-fire" exercises performed on human cadavers. Although the
correlation was strong, the response of the sternum in the model exhibited large
oscillations, which were not observed in the cadavers. It is believed that this occurred as
a result of the lack of damping in the model. Soft tissues, such as the skin and muscle,
were incorporated into the model for the present study to supply damping for these
oscillations.
The only existing cadaveric study on the biomechanical response of the thorax to
bullet impacts was performed by DeMaio, et al at the Armed Forces Institute of
Pathology. [Ref. 13] In their studies, cadavers were protected with a bulletproof vest
incorporating either soft armor alone or soft armor plus one of two variations on a
ceramic plate. These cadavers were then struck with either a NATO 9mm round or a
NATO 7 .62mm M80 ball round fired from a distance of 50 feet. Various parameters
were recorded including the accelerations of the sternum, spine, and carina, and the left
and right ventricular pressures. Post-shot autopsies were performed to judge injury and
43
assess survivability. The model utilized in the present study was created in an attempt to
obtain similar results from finite element analysis for these parameters, dependent upon
the projectile and body armor used. As such, the boundary conditions and loads applied
in our study were derived from the test parameters used at AFIP.
44
III. FINITE ELEMENT MODEL
A. HUMAN THORACIC BODY MODEL
The human thorax presents a myriad of modeling problems for the researcher.
Along with the complex geometries of the various ribs themselves, there are multiple
connections, such as the articular cartilage between the rib pairs and the vertebrae that
must be accurately modeled to create a viable model. In addition, the material properties
of the ribs are not constant along their entire length. This adds an additional level of
complexity to the model. Another fundamental concern is the wide variation that may
take place between individuals. Thus, the correct material properties for a 20-year-old
male are unlikely to match those of a 70-year-old female. In the model created for this
study, depicted in Figure 21 below, all the finite element position nodal data were taken
from work by Andriacchi, et al [Ref. 19] and Roberts and Chen [Ref. 17], which was later
adapted by Hughes [Ref. 18].
1. Ribs
The modeling of the ribs was an ar{'.a of some difficulty due to their complex
shape and material properties. The size and shape of the ribs correspond to that of a
smaller, female build. Each rib is represented by thirteen beam elements. A larger
number would have been prohibitively costly in terms of computation time. Each
element is given a specified cross-sectional area dependent upon its distance from the
spine. This enables the correct size, shape, and angle of the head, tuberosity,
midauxillary line junction, costrachondral joint, and stemochondral junction to be
45
modeled. In addition to the geometry of the ribs, each element had to have its material
property specified. The values used were based on the work done by Y ogananda and
Pintar [Ref. 20], who utilized three point bending experiments to determine material
properties for the seventh and eighth rib of multiple subjects. Their "average" values
were used to determine the approximate material properties for each element of each rib
pair. The ribs were assumed to be composed of only compact bone and were modeled as
a linear elastic material. The Young's Modulus chosen was 2.83 GPa; a density of 1000
kg/m3 and a Poisson's ration of 0.2 were used.
Figure 21: Plot of Sternum, Ribs, Spine, and Cartilage
2. Spine
Due to the nature of this study, the complexities of the spine were not
fundamental to the research being conducted. As such, the spine was modeled by a series
46
of beam elements, based on previous experiments. [See Refs. 21and22] Each modeled
vertebra consisted of two beam elements, with an intervening beam element between
adjacent vertebra to model the intervertebral disc. The facet joints were modeled by
connecting two beam elements, one from the midpoint of each adjacent vertebra. Figure
22 below depicts how the spine was modeled. The material properties for the vertebrae
and the vertebral disc derived from work done by Sundaram and Belytschko [Ref. 23].
The vertebra and facet joints were modeled with a Young's Modulus of 12.13 GPa, a
density of 1000 kg/m3, and a Poisson's ration of 0.2. The intervertebral discs were given
the following material properties: Young's Modulus: 1.5 GPa, Density: 100 kg/m3, and
Poisson's ration: 0.2.
47
Figure 22: Medial View of the Ribs and Spine
3. Sternum
The sternum, as seen in Figure 23 below, was modeled with a series of twelve
thin shell elements. Each element was given a specified thickness of 0.25 inches (0.63
cm) to create the three-dimensional model. The material properties for the sternum were
derived from the compact bone properties of rib 4. As such, the sternum's Young's
Modulus was 12.13 GPa, density was 1000 kg/m3, and Poisson's ration was 0.2.
48
4. Muscle
\ - \
\ I
I \ /
Figure 23: Sternum Shape in Thorax Model
The modeling of the muscle, which is shown in Figure 24, was done with 24
solid elements. The elements varied in thickness from 0.25 inches (0.63 cm) along the
central, anterior edge of the sternum to a maximum of2.35 inches (5.97 cm) at the most
distal position of rib #4. This accurately models the correct curvature of the muscle along
the anterior side of the thorax. The material properties of muscle were modeled with a
viscoelastic material type. (See Refs. 24, 25 and 26 for a discussion on viscoelasticity.)
The material property values utilized were a density of 950 kg/m3, a bulk modulus of 5 x
105 Pa, a short-time shear modulus of 1 x 105 Pa, a long-time shear modulus of 1 x 104
Pa, and a decay constant of 1000. The equation used to calculate the shear relaxation
behavior is as follows:
49
B.
G(t) = Shear Modulus Go = Short-Time Shear Modulus Goo = Long-Time Shear Modulus p = Decay Constant
This time-dependent shear modulus relationship is explained further in Appendix
Figure 24: Muscle as Constructed in Thorax Model
5. Cartilage
The cartilaginous connections of the thorax were modeled with beam elements, as
depicted by the darker lines in Figure 25 below. A single beam element was used to
50
model the stemochondraljoint whereas two beam elements were utilized to model the
articular cartilage between the rib and the vertebrae. The material properties of the
cartilage at the stemochondral junction were given values of 64. 7 MP a for Young's
Modulus, 1000 kg/m3 for density, and 0.2 for Poisson's ratio. Material properties for the
chondracostal cartilage were a density of 1000 kg/m3, a Young's Modulus of 5 MPa, and
a Poisson's ratio of 0.2. Additionally, a series of vertical cartilaginous connections at the
inferior edge of the sternum, modeled as beam elements, were used to create the
subcostal angle.
--- ·-
-c··.·.· --7/•
~ I \
Figure 25: Articular Cartilage Connecting Sternum and Ribs
51
B. BODY ARMOR
The body armor itself consisted of a plate of CBA (concealable body armor)
composite material and sheet of Kevlar. Due to the proprietary nature of these materials,
the determination of their material properties was subject to some guesswork. However,
realistic values were used throughout the study. The material properties of Kevlar were
assumed to be a density of 1440 kg/m3, a Young's Modulus of 1 GPa, and a Poisson's
ratio of0.2. The CBA plate was given a density of2500 kg/m3, a Young's Modulus of
448 GPa, and a Poisson's ratio of 0.2. In one investigation that was undertaken, a plate
of CBA composite material was modeled with 126 thick shell elements. The thickness of
this plate was set as 0.5 inches (0.51 cm). This plate was directly attached to a sheet of
Kevlar, modeled by 126 thick shell elements as well and a thickness of 0.25 inches (0.63
cm). This sheet was modeled such that it projected directly across from the most anterior
points of the muscle tissue as noted below in Figure 26. This created a gap between the
muscle and the Kevlar above the sternum, which is an accurate representation of the
actual placement of the vest when worn. In another investigation, the CBA plate was
removed to simulate the usage of just soft armor.
52
Figure 26: Depiction of Kevlar Vest Overlaying Muscle
C. INTERFACE ELEMENTS
In order to prevent rigid body motion of the body armor after bullet impact,
several contact elements had to be added to the model. The interface between the vest
and the muscle was modeled with a tied-type contact element. This allows for the
movement of the vest in one direction to impart a force onto the muscle, while movement
in the other creates a separation between the two parts without any transfer of force.
Additionally, springs and dampers were added between the muscle and the ribs. This was
necessary to portray the correct viscous nature of the muscle and its corresponding
transfer of force to the ribs. This also suppressed spurious oscillations in the sternum.
53
D. PROJECTILE
Due to inherent problems with the analysis, more than one set of contact elements
was not possible. Thus, it was not possible to insert contact elements between the bullet
and the body armor. Therefore, the projectile was given the correct mass and shape and
was attached directly to the most anterior body armor component. This was either the
CBA plate or the Kevlar sheet, depending upon the test being run. It is visible as the
single element on the left side of Figure 27. The projectile was modeled as a single solid
element and given the dimensions and material properties of either a NATO 7 .62 mm
Ball M80 round or a NATO 9 mm full metal jacket round. In order to model the motion
of the projectile, the most anterior four nodes of the projectile were given an initial
velocity. This imparted a momentum to the bullet that was transferred to the body armor
in a manner consistent with that of bullet impact analysis. The material properties of the
projectile were based on a linear elastic material, with the Young's modulus and density
corresponding to that of steel. The initial velocity of the projectile was determined
experimentally during test firings at the Aberdeen Proving Grounds in Maryland. [Ref.
13] These numbers (2900 f/s for the 7.62mm round and 1500 f/s for the 9mm round)
were used in the DYNA3D input file. By directly modeling the motion of the bullet, it
was possible to avoid errors which might occur in an attempt to model a forcing function
to apply to the body armor.
54
l
Figure 27: Medial View ofCBA Plate and Kevlar Vest
E. BOUNDARY CONDITIONS
The boundary conditions that were chosen were based on the experimental set-up
during the cadaveric studies at Armed Forces Institute of Pathology. [Ref. 13] In their
experiment, cadavers were laid flat on a wooden board and secured to it via wires. To
approximate this set-up, the most posterior nodes of the thoracic model were constrained
to prevent translations. It is believed that this would adequately model the experimental
set-up.
55
F. ANALYSIS CODE
After the finite element model had been created, it was put into the input deck
specifications for DYNA-3D, a finite element analysis program available from Lawrence
Livermore National Laboratories. The particular version utilized was DYNA-3D version
N-12, compiled on 10-03-98. This software was run on Silicon Graphics International
OCTANE workstations running IRIX 6.4.
56
IV. RESULTS AND DISCUSSION
After construction of the finite element model and imposition of the boundary
conditions and initial velocities for the projectile, an analysis was run for a model time
duration of two milliseconds. The DYNA3D input deck was designed to output the
acceleration, velocity, and displacement in the anterior to posterior direction for the
center of the sternum as well as the T7 vertebra. These locations correspond to those
used by DeMaio, et al at AFIP [Ref. 13]. Data obtained from the DYNA3D analysis was
subsequently smoothed using a simple twelve-point averaging method to remove aberrant
oscillations. The experimental data from DeMaio, et al [Ref. 13] was obtained as text
files with the time and value listed and did not require processing before comparison.
The model was analyzed with two variations. The first was that of the 7 .62mm projectile
impacting on a vest constructed of Kevlar and a CBA (concealable body armor) plate.
The second was the impact of a 9mm projectile into a body wearing only the Kevlar vest.
For purposes of validation, the acceleration information was used as the primary
comparison data between that from DYNA3D and that obtained from AFIP. This was
due to the use of numerical integration by the experimenters at AFIP to obtain the
velocities and displacements. In order to set a standard for comparisons, the
characteristics that were focused upon were the times and magnitudes of the first peak
and trough, and the trend of the parameter at the end of the analysis period.
57
A. VIABILITY STUDY
1. CBA Plate, Kevlar Vest, and NATO 7.62mm ball M80 Round
This test case utilized the NATO 7.62mm M80 ball round as the projectile, with
an impact velocity of 966 mis. This velocity is consistent with those obtained by
DeMaio, et al from a chronometer during their test firings [Ref. 13]. The vest consisted
of a layer of Kevlar and a CBA plate. The time duration of the model analysis time was
five milliseconds.
The following figures (see Figures 28 through 33) display the results that were
obtained from the DYNA3D analysis versus those results obtained experimentally [Ref.
13]. They include comparisons of sternum and spinal accelerations, velocities, and
displacements in the anterior to posterior direction. This direction is chosen because it is
the direction of the projectile upon impact.
The match between the experimental sternal acceleration data and the computer
model was excellent for this case, as illustrated in Figure 28. The magnitude of the initial
peak is of the right order, the location of the first peak and troughs are at the right time,
and the long-term behaviors are similar. The only discrepancy occurs at approximately
one millisecond. Postmortem examinations revealed that massive sternal fractures had
occurred in this case. These fractures would significantly reduce the stiffness of the
sternum and allow for greater accelerations, hence a greater magnitude of the trough, than
those predicted by the DYNA3D analysis. This is because there are no failure modes
included in the DYNA3D model allowing for bone fractures. Otherwise, there was an
excellent correlation between the two cases. In this particular case, the analysis was run
58
for five milliseconds. However, due to the long computer processing time necessary, as
well as the consideration that the most important responses occurred in the first two
milliseconds, all subsequent analyses were run for a shorter model time of two
milliseconds.
:§ c: 0
~
i
2000
1500
1000
500
-500 • !
f j
Sternum Acceleration
I-·- ~~(#801) I
-1000 .____. _ __.._....__._ _ _._ _ _._ _ _._ _ _,._ _ _.__ _ _.______. 0 0.5 1.5 2.5 3.5 4.5
Time(ms)
Figure 28: Sternum Acceleration (CBA & Kevlar). After Ref. [13].
The data for the sternum velocity did not match as well as expected. In their
original investigation, DeMaio, et al [Ref. 13] only recorded the accelerations and then
used numerical integration to obtain the results for the velocities and displacements. As
such, the acceleration data will be considered more fundamental to validation. In this
particular example (see Figure 29), the general shapes of the velocity curves match well.
However, there exists some doubt about the initial response of the sternum immediately
upon impact, due possibly to instrumentation error or interference effects. The initial
59
acceleration if in the opposite direction to the impact direction. Consequently, the data
obtained for the sternum acceleration at the immediate time of impact may not be
completely accurate (See discrepancy in first 0.2 milliseconds in Figure 28). This
discrepancy then propagates through to the estimations of the displacements and
velocities due to the use of numerical integration. As such, in the sternum velocity graph,
the initial downward motion of the experimental results, dependent upon the initial
negative acceleration in the first 0.2 milliseconds in Figure 28, is questionable. The
separation that this initial motion creates is carried through the rest of the analysis. If this
initial separation were discounted, the match between the two would be excellent.
DeMaio, et al [Ref. 13] estimated about 30 millimeters of displacement at the
sternum at approximately 30 milliseconds from experimental observation even though
there was no direct measurement of the displacement. However, the results displayed
(see Figure 30) below do not show this displacement. They obtained this displacement
value at the end of their data recording period, at approximately 30 milliseconds. Due to
the computer time required to run an analysis for this length of time, the period of
investigation was limited to five milliseconds with the final displacement to be
extrapolated from the resulting data. As the velocity begins to approach zero at the end
of the five millisecond period, the displacement will obtain a steady-state value.
Extrapolating from the available results leads to an estimation of between 25 and 30
millimeters of displacement, corresponding to the results obtained by DeMaio [Ref. 13].
60
Sternum Velocity
I-·_ ~§'}..(#801) I 10
8
~ 6
Figure 29: Sternum Velocity (CBA & Kevlar). After Ref. [13].
Sternum Displacement
I -· _ ~§'}..(#801) I 20
15
-5
-10~-~-~-~-~-~-~-~-~-~-~
0 0.5 1.5 2.5 3.5 4.5 Time (ms)
Figure 30: Sternum Displacements (CBA & Kevlar). After Ref. [13].
61
The comparison between the spinal acceleration results from the computer model
and the experimental data also correlated well, as depicted in Figure 31. The magnitudes
are approximately the same and the points of inflection are located at similar times. The
discrepancy between the magnitudes lends credence to the idea that the model is too stiff.
However, this is an inherent problem in the finite element method and does not detract
from the validity of the computer model. Additionally, it is important to note that the
correlation is excellent until one millisecond. It is believed that the separation after this
point is due to the massive sternal fractures that occurred and the resulting higher
accelerations in the sternum than those predicted by DYNA3D. Because the forces
imparted from the impact on the anterior face of the thorax must propagate through the
connective and soft tissues as well as the skeleton to affect the spinal acceleration, these
fractures in the sternum have a direct consequence on the acceleration of the spine.
However, due to the same overall trends being predicted, the high degree of correlation
lends validity to the constructed model. This correspondence is also noted in the
predicted and experimental values for the spinal velocities (see Figure 32) and
displacements (see Figure 33).
62
30
20
10
§ 0 ........ § ~ §-10 <(
-20
-30
-40
0.5 1.5
Spine Acceleralion
· ... · 2.5
Tirne(ms} 3.5 4.5 5
Figure 31: Spinal Acceleration (CBA & Kevlar). After Ref. [13].
Spinal Velocity 0.1 r---,.---....----,---.-----.---r----.--..---.....---.
-0.1
-0.2
i-0.3
2::-·g ~ -0.4
-0.5
-0.6
-0.7
-0.8 0 0.5 1.5
I -· _ ~~ (#801) I
· .•.......... ··
2.5 3 nme(ms}
.... ······················-·--...
.. ··
3.5 4.5
Figure 32: Spinal Velocity (CBA & Kevlar). After Ref. [13].
63
'E §.
--0.2
--0.4
i --0.6 E
?J ~ --0.8 0
-1
-12
-1.4
0.5
Spinar Displacement
·····-··························· .•.
1.5 2.5 Time(ms)
I -· _ ~~ (#801) I
···········•····· ...
3.5 4.5
Figure 33: Spinal Displacement (CBA & Kevlar). After Ref. [13].
2. Kevlar Vest and NATO 9mm Round
This test case utilized the NATO 9mm full metal jacket round as the projectile,
with an impact velocity of 500 mis. The armor vest consisted of only a layer of Kevlar.
The analysis time duration was two milliseconds.
The correlation between the results from DYNA3D and those of DeMaio [Ref.
13] were high for this case as well, as seen in Figures 34 through 39 below. There are
some minor discrepancies in the prediction of the sternum acceleration, but these can be
attributed to the inherent stiffness of the finite element method. In Figure 34 below, note
that the locations for the first and second peak match exactly. Unfortunately, the
magnitudes of these peaks were clipped in the experimental data, yet extrapolation from
the available data suggests that the magnitudes would match very well. It is believed that
64
the method by which the accelerometer was mounted accounts for the discrepancy noted
at approximately 0.9 milliseconds in Figure 34. Securing the accelerometer to the
posterior side of the sternum with a length of string allows for accurate measurements of
acceleration as the sternum moves in the posterior direction, but stretching of the string
under anterior acceleration of the sternum may create the noted discrepancy.
Additionally, the massive sternal fractures noted in the previous validation case are not
noted in post-mortem report for this test case. As such, the magnitude of the
experimental response at the first trough does not exceed that predicted by the DYNA3D
analysis. However, the long-term behavior of the DYNA3D predictions and those
obtained experimentally match well, with both approaching zero. For this test case,
similar to the first, the discrepancies noted in the acceleration data propagate through to
the predictions of velocity and displacements due to the use of numerical integration.
There is a significant deviation between the experimental results and those predicted by
DYNA3D for the spinal acceleration, velocity, and displacements. Although the
possibility for instrumentation error, such as incorrect mounting of the accelerometer
during the cadaveric studies exists, the most logical explanation for the discrepancy is
due to problems with the boundary conditions. The experimental method utilized called
for securing the cadaver to a backboard by a simple wire wrapping around the body and
backboard. This may have allowed for movement of the cadaver that the boundary
conditions imposed on the FEA model would have made impossible. This movement
would have a more pronounced effect on the spinal data rather than that of the sternum
due to the presence of the backboard limiting the movement of the spine whereas no such
65
restrictions would exist on the sternum. Additional to the boundary conditions, simple
mechanics dictates that the high accelerations imposed on the thorax should result in
higher magnitude accelerations in the spine than those actually reported. As such, we do
not feel that there is any need to question the viability of our model. Rather, the
consistent behavior of our model under these various load conditions lends credibility to
it. A comparison between Figure 31 and Figure 37, the spinal accelerations for the two
test cases, illustrates the consistent behavior of the FEA model. The shape predicted
through FEA in the second test case (Figure 3 7) matches well with that experimentally
determined in test case one (Figure 31 ). This indicates that the model performed
consistently and lends credence to a boundary condition mismatch between the
experimental work and the FEA modeling.
Sternum Acceleration 3000 .-----.---,---..---.---.---..----r---,---..---.
I -· _ ~~ (#678) I
..
:§ 1000
c: 0
~ 500
§ <
-500 . ____ , ..... -1000
-1500
-2000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Time(ms)
Figure 34: Sternum Acceleration (Kevlar only). After Ref. [13].
66
Sternum Velocity
I -· _ ~~ (#678) I 10
8
4
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time(ms)
Figure 35: Sternum Velocity (Kevlar only). After Ref. [13].
Sternum Displacement
I -· _ ~~ (#678) I
10
0.6 0.8 1 1.2 Time(ms)
Figure 36: Sternum Displacements (Kevlar only). After Ref. [13].
67
Spine Acceleration
I -· - f§'J.. (#678) I
!----~--..:..········ .... . . . . . . .
-5
:g-10 c: .2 "Ei-15
§ <-20
-25
-30
-35
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (ms)
Figure 37: Spinal Acceleration (Kevlar only). After Ref. [13].
Spinal Ve10c1ty 0.1----------------------
. . . . . . . . . . .
--0.1
. . .
I -· - f§'J.. (#678) I
.............. . . .. .
--02 .___....__ _ _,__ _ _._ _ _._ _ __._ _ __.. _ ___;L--_..t.__ _ _,___j
0 0.2 0.4 0.6 0.8 1 1.2 1.8 1.4 1.6 Time (ms)
Figure 38: Spinal Velocity (Kevlar only). After Ref. [13].
68
Spinal Displacement
. . . . .
-6
I -· _ ~~ (#678) I
. . . . . . . . . ... . . .
-10~~-~-~-~-~-~-~-~-~~
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time(ms)
Figure 39: Spinal Displacement (Kevlar only). After Ref. [13].
B. PARAMETRIC STUDY
In order to gain a better understanding of the constructed model, a parametric
study was conducted. Parameters such as the Young's Modulus of the sternum, muscle,
Kevlar, CBA (concealable body armor) plate, sternal cartilage, and intervertebral disc
were changed individually to assess their importance to the overall behavior of the model
through comparisons with the Kevlar and CBA plate case presented above. Due to the
use of numerical integration of the experimental data to obtain the velocities and
displacements, the accelerations were considered the most important element for
comparison. Through this study, the muscles, the Young's Modulus of the sternum
articular cartilage and of the skeleton in general, the contact elements and gap between
69
the vest and the sternum, the size of the thorax, and the densities of the CBA and Kevlar
were determined to be the most important factors in determining the correct behavior of
the model. The following graphs are those that were obtained after changing one of the
factors listed above. Note that in Figures 40 and 41, as in all subsequent figures, the three
items graphed are the experimental results obtained by DeMaio, et al [Ref. 13], the
results from DYNA3D for the first validation case (CBA plate, Kevlar vest, and NATO
7.62mm round), and the results returned from DYNA3D with one of the parameters
changed. All of the test cases conducted are included in Appendix A.
The most important element in the behavior of the model was the inclusion of
muscle. Removing the muscle from the model had serious ramifications to the predictive
power of the biomechanical response. It is believed that the muscles provide much of the
damping and viscous effects that are essential to reduce the high forces that are imparted
to the body upon impact. (Recall that the muscles were modeled as a viscoelastic
material.) Additionally, muscle damping suppresses the high frequency oscillations that
would otherwise dominate the dynamic response following impact. The graphs below,
Figures 40 and 41, depict the results that were obtained for the sternum and spinal .
accelerations with the muscle removed from the Kevlar and CBA plate case.
70
4
3
2
1
1
2
-3
--4 0
,(\ I ~
~ 1 ~~r
0.2 0.4
Sternum Acceleration
" Exp (#801)
-- FEA + Validation Case
lit--
0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time(ms)
Figure 40: Sternum Acceleration (Kevlar and CBA plate without muscle). After Ref. [13].
Spine Acceleration
Exp (#801) FEA
+ Validation Case
-5
-10
g ~-15
I -20
-25
-30
-35~-~-~-~-~-~-~--~-~-~-~ 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Time(ms)
Figure 41: Spinal Acceleration (Kevlar and CBA plate without muscle). After Ref. [13].
71
Another important element in the construction of a viable model was the dampers
between the muscles and the ribs. Although they were modeled as separate elements in
the model, the dampers and the muscles, combined, were both required to accurately
model the viscoelastic behavior of human skin and muscle. The majority of the damping
occurred in the muscles themselves, as depicted in Figure 40, but the dampers were also
required to ensure the correct behavior in the model, as evidenced in the following
graphs. The graphs depict the DYNA3D results for a model without the damping
discrete elements. Note that the trough depicted in the sternum acceleration in the
validation studies is missing and that the behaviors of the experimental data and the
DYNA3D results at the end of the analysis time do not match well. Although the point of
inflection is at the same time in the spinal acceleration comparisons, the magnitudes do
not correlate well.
72
2000
1500
1000
:§ c: 0
~ 500 ., ~
-500
Sternum Acceleration
0.8 1 1.2 Time(ms)
Exp (#801) FEA
+ Validation Case
1.4 1.6 1.8
Figure 42: Sternum Acceleration (Kevlar and CBA plate without dampers). After Ref. [13].
c: 0
Spine Acceleration s...-~-.-~-,-~--,-~---,r--~.,-~-.-~-.~--,.~~r--~
Exp (#801) FEA
+ Validation Case
-5
-10
~-15
I -20
-25
-30
-35'--~-'--~-'-~-'-~---'~~.L-~--'-~-'-~-"-~--'~~ 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Tima(ms)
Figure 43: Spinal Acceleration (Kevlar and CBA plate without dampers). After Ref. [13].
73
The Young's Modulus of the muscle was also varied to determine its effect on the
biomechanical behavior of the thorax model. In the following case, the Young's
Modulus was increased by a factor of five from its original value. This increase in the
modulus leads to an increase in the speed of sound calculated for the model according to
the following equation:
V5 = Speed of sound E =Young's Modulus p =Density
The increase in the speed of sound results in an increase in frequency response for the
model as illustrated below in Figures 44 and 45. Thus, the locations for the first peak and
trough in the sternum acceleration data are not the equivalent. Additionally, the change
in the Young's Modulus also increases the magnitude of the first peak predicted by
DYNA3D. There are no notable changes noticed in the behavior of the spine with this
change in muscle Young's Modulus.
74
Sternum Acceleration 2000 .--.,.---,---,---.--r--.---,---,-----,---,
-500
·· .. ·,,
Exp (#801) FEA
+ Validation Case
... ,.a··
... · .. ...
,,,-1i" -1000~-~-~-~-~--~-~~~-~--~-
o 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time<ms)
Figure 44: Sternum Acceleration (Kevlar and CBA plate with muscle Young's Modulus increased by five times). After Ref. [13].
Spine Acceleration 5r---.---,----r----.:----r---.---,----r--r--
Exp (#801) FEA
+ Validation Case
-5
-10 § c: .2 ~-15
~ -20
-25
-30
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time<ms)
Figure 45: Spinal Acceleration (Kevlar and CBA plate with muscle Young's Modulus increased by five times). After Ref. [13].
75
A significant response was also noted for an increase in the Young's Modulus of
the sternal articular cartilage. Due to the .direct contact between the vest and the sternum
via the muscle, a ten-fold increase in the Young's Modulus of the articular cartilage does
not have any effect on the acceleration of the sternum. However, because of the
connection of the sternum to the ribs through the articular cartilage, the change in the
Young's Modulus does affect the response of the spine as illustrated in Figure 47 below.
Note that the point of inflection has advanced from approximately 0.7 milliseconds to 0.2
milliseconds. Additionally, the change in Young's Modulus introduced several new local
maxima and minima in the predicted acceleration of the spine.
Sternum Acceleration
1500
-500 .
Exp (#801) FEA
+ Validation Case
, ..........
, .. "'· -1000'-----'----'----'----'---'---'='---'----'---~~
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time (ms)
Figure 46: Sternum Acceleration (Kevlar and CBA plate with sternal cartilage Young's Modulus increased by ten times). After Ref. [13].
76
-5
-10 :§ g ~-15
I -20
-25
..,'JO
Spine Acceleration
...... +
Exp (#801) FEA Validation Case
..,'35'-----'~--'-~-'-~--'-~-'-~-'--~-'-~-'--~-'-----' 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Time(ms)
Figure 47: Spinal Acceleration (Kevlar and CBA plate with sternal cartilage Young's Modulus increased by ten times). After Ref. [13].
Another important parameter was deemed to be the contact elements between the
muscle and the vest. The contact elements provide a link between these two independent
objects. Without the contact elements, the vest would move with rigid body motion and
not interact with the thorax at all. In this case, the contact elements immediately between
the sternum and the vest were removed, while those surrounding the sternum were left in
place. The resulting response in the sternum (see Figure 48) indicates that the motion is
directly dependent upon the direct transfer of force from the vest to the sternum. Thus,
without the contacts to help in this transfer, the behavior in both the sternum and the
spine is altered significantly. Note that the magnitude of the predicted response at the
first peak in the sternum acceleration has decreased from the standard case and that the
trough has disappeared. In addition, the behaviors at the end of the analysis period
77
deviate with the predicted response indicating a constant decrease in acceleration and the
experimental results depicting a return to zero. Also, observe that the spinal accelerations
(Figure 49) are not effected by this change in the model. This suggests that a significant
path of force propagation influencing the behavior of the spine comes directly from the
muscle attached to the lateral edges of the thorax.
Sternum Acceleration
1500
~ ~\
: + ·- ...... '414-i!!- ·.,it ·-- ·• "!";+; a +""~ · ...... ~,-.
·~ 500 +'fll- • * " ~ +
1000
-500
Exp (#801) FEA
+ Validation Case
.........
.. ..
;·:" -1000 L....__L..-_L..__L..__L..__L..__"""'-----'-----'---'-----'
0 0.2 0.4 0.6 0.8 , 1.2 1.4 1.6 1.8 Time(ms)
Figure 48: Sternum Acceleration (Kevlar and CBA plate with contact elements removed). After Ref. [13].
78
.......
-5
-10
g
Spine Acceleration
+
Exp (#801) FEA Validation Case
~-15
J -20
-25
-30
-35'-----'~--'-~-'-~--'-~---'-~-'-~-'--~,__~,____,
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time(ms)
Figure 49: Spinal Acceleration (Kevlar and CBA plate with contact elements removed). After Ref. [13].
The properties of the materials of the body armor vest were also investigated.
The densities of both Kevlar and the CBA plate were increased to determine their effect
on the response of the thorax. Both the spinal and sternum accelerations (see Figure 50
and Figure 52) were decreased in peak magnitude and frequency. In addition, the trough
observed in the validation study is not observed in either case reported here. The
frequency effect can be attributed to the speed of sound equation reported above. The
magnitude effect is dependent upon simple Newtonian mechanics. Since the force
remains constant and the mass increases due to the increase in density, the acceleration
must go down. Due to the decrease in force propagated to the anterior thorax by the vest,
the consequent magnitude of the response in the spine is also decreased (see Figure 51
and Figure 53); however, the time of the point of inflection does not change. This is
79
consistent with the results obtained from the parametric study. The point of inflection in
the spine is dependent upon the material properties of the elements that directly transfer
this force. Since the properties varied in these cases are not directly in this path of force
propagation, there is no effect on the time of the point of inflection.
Sterrum Acceleration
1500
-500
Exp (#801) FEA
+ Validation Case
, ..........
, .•. l -1000 '----'------''------'---'----'----'-""'---'----'-----'----'
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time(ms)
Figure 50: Sternum Acceleration (Kevlar and CBA plate with Kevlar density increased five times). After Ref. [13].
80
Spine Acceleration
Exp (#801) FEA
+ Validation Case
-5
-10 § c: .2 ~-15
I -20
-25
-30
0.8 1 1.2 1.4 1.6 1.8 Time(ms)
Figure 51: Spinal Acceleration (Kevlar and CBA plate with Kevlar density increased five times). After Ref. [13].
Sternum Acceleration 2000
Exp (#801) FEA
+ Validation Case 1500
1000 ~ -#Ir.JI!.;. 'Iii-
.--4-...... ~ § • + ·- ..-..'114-c: .j!!, • .,it ·-- ... 7;+; ' *++ 0 "!ffi.~ +)!J!t11'+ ~ .l!! +"". ~\-iii'+ § ·.' < .... +
...... 1l¢i.
\ .... __ ,,.~ -500 ' .· ... ·
.:· '·, ;
-1000 ,,,,.··
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time(ms)
Figure 52: Sternum Acceleration (Kevlar and CBA plate with CBA plate density increased five times). After Ref. [13].
81
.........
-5
-10 § c:
Spine Acceleration
+
Exp (#801) FEA Validation Case
~-15
I -20
-25
-30
-35~~~~~~~~~~~~~~~~~~~
0 0.2 0.4 0.6 0.8 , 1.2 1.4 1.6 1.8 Time(ms)
Figure 53: Spinal Acceleration (Kevlar and CBA plate with CBA plate density increased five times). After Ref. [13].
In order to understand the effect of the size of the individual on the effectiveness
of the body armor, the thorax dimensions were increased by 25%. The vest size was kept
constant to eliminate that as a variable. The response of the sternum demonstrates a
similar response as that of the increased density of the CBA plate or Kevlar with the
corresponding lack of a trough and decreased magnitude of the first peak. (See Figure 54
below.) It is thought that this is due to the increase in size of the sternum itself. As the
sternum size increases, it becomes more massive. Thus, it will have a smaller
acceleration due to Newton's Second Law. Additionally, the decreased magnitude of the
response in the spine can be attributed to similar effects. Due to the increase in body
size, the distance of stress propagation through the ribs plus the increased mass of the ribs
themselves limit the magnitude of the response in the spine. In addition, the increased
82
size of the thorax creates a longer path of propagation for the force to reach the spine.
This results in a later point of inflection (1.2 milliseconds versus 0.7 milliseconds) than
that noted in the validity studies. (See Figure 55 below.)
Sternum Acceleration
1500
1000
-500
Exp (#801) FEA
+ Validation Case
/ ... · ... ·
,,,.,,. .. "'· -1000~-~-~~~~-~-~~~-~-~-~
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time(ms)
Figure 54: Sternum Acceleration (Kevlar and CBA plate with thorax dimensions increased 25%). After Ref. [13].
83
Spine Accelerarion
Exp (#801) FEA Validation Case
-5
-10
c: ,g ~ -15
~ -20
-25
-30
0.2 0.4 0.6 0.8 , 1.2 1.4 1.6 1.8 Time(ms)
Figure 55: Spinal Acceleration (Kevlar and CBA plate with thorax dimenstions increased 25%). After Ref. [13].
84
V. CONCLUSIONS/RECOMMENDATIONS
A. CONCLUSIONS
The research described in this thesis was undertaken to investigate the
construction of a finite element model to model the effects of impact loads to a human
thorax wearing a body armor system. The overriding goal for this study was to obtain a
viable model of the human thorax that could be used to adequately predict the
accelerations experienced by a body subjected to impact by a projectile, namely a bullet.
After construction of the model, two studies were undertaken. The first was to prove the
viability of the model. The results demonstrated that the model adequately matched the
available experimental data for both load cases imposed. As such the model was deemed
to be viable, and a parametric study was then undertaken to determine the critical
components of the model. This analysis determined that the damping properties of the
muscles were the most important element in the model. Hughes [Ref. 18] had presented
a model for the prediction of human thorax response to impact loads; however, by not
including this essential element, his model suffered from oscillations and, therefore,
lacked the quantitative predictive power demonstrated through this study. The inclusion
of the musculature into the finite element model provided for the good correlation
between the FEA results and the experimental data.
Additional elements were deemed significant in establishing the correct model of
the thorax, including the Young's Moduli of the sternum articular cartilage and the bones
and the initial gap between the vest and the sternum. The parametric study demonstrated
85
that the method of stress propagation from the body armor system to the sternum was
direct, via the layer of muscle over the sternum and consequently through the ribs and
sternochondral cartilage to the rest of the body. Therefore, variations in the stiffness of
these elements, namely alterations in the Young's Modulus, resulted in significantly
different responses in both the sternum and the spine. Additionally, this method of stress
propagation was dependent upon the initial gap between the sternum and the bulletproof
vest. Thus, removal of this space resulted in a different method of force transference,
leading to a different predicted behavior.
The final consideration in the construction of this model was with the material
properties chosen for the body armor system itself. One of the experimental setups used
by DeMaio relied on a Kevlar vest with a Concealable Body Armor (CBA) ceramic plate
to prevent bullet penetrations. Due to the proprietary nature of these materials, it was
difficult to obtain accurate properties; however, reasonable values were chosen. The
parametric study demonstrated that the densities of these materials are paramount to the
behavior of the human thorax under impact. Thus, use of another body armor system for
protection could have significant effects on the responses of the body to impacts.
B. RECOMMENDATIONS
made.
Although this model has excellent predictive powers, several refinements can be
• This model lacks the soft inner tissues of the thoracic cavity. It is possible
that there is an element of stress propagation through the soft tissues, such as
86
the heart and lungs, into the spine, though the majority will likely be found to
be through the skeletal structure of the thorax. The inclusion of these tissues
is unlikely to radically change the responses predicted for the spine, but their
inclusion is important in creating a complete thoracic model. Additionally,
the various ligaments, tendons, and minor muscles of the thorax are not
included in this model. These soft tissues are more likely to directly influence
the response predicted by this model as they regulate the method by which
forces are transferred between the various elements of the thoracic skeleton.
As such, they are important elements to be included in a refined model of the
human thorax.
• A perpetual need in biomechanical modeling has been adequate research into
the material properties of the human body, including densities and Young's
moduli of the bones and cartilage. Unfortunately, there exists a dearth of
reliable data in this area. Previous sample sizes in existing studies have been
too small to adequately obtain average values for the population at large.
Additionally, no studies have been discovered that examined the material
properties of muscle in detail. These are important aspects in predicting the
correct behavior for the thorax upon impact and serious consideration should
be given to further research in that area.
• Due to computer processor limitations, the number of elements in the thorax
were kept to a minimum necessary to adequately model the structure.
87
However, increasing the number of elements could further refine the predicted
behaviors of the biomechanical model.
• Due to the focus of this study on using the experimental data obtained by
AFIP for validation, it is important to understand the parameters they used in
their study. This includes more investigations into the material properties of
the protective body armor, the boundary conditions imposed by their methods,
and the exact positions, orientations, and manner in which they secured the
instruments to the structures studied.
• A better approximation of the musculature of the anterior facet of the thorax
is also necessary. As this study demonstrated, the behavior of the model is
intimately linked to the shape and material properties of this muscle tissue.
An such, it is important to refine the meshing of the muscle and obtain
experimental data, if possible, on the exact geometries.
• Inclusion of a failure mode for the bones is essential to accurately model the
responses expected in the human thorax upon impact. Due to the changes in
stiffness that occur as a result of a fracture, the mechanism for stress
propagation may alter leading to a significantly different prediction for the
thorax response.
88
LIST OF REFERENCES
I. Brauer, J. R., (Editor), What Every Engineer should know about Finite Element Analysis, 2nd ed., Marcel Dekker, 1993.
2. Cook, R. D., Malkus, D. S., & Plesha, M. E., Concepts and Applications of Finite Element Analysis, 3rd ed., John Wiley & Sons, 1989.
3. Huebner, K. H., Thornton, E. A., & Bryom, T. G., The Finite Element Method/or Engineers, 3rd ed., John Wiley & Sons, 1995.
4. Akin, J., Finite Element Analysis for Undergraduates, Academic Press, 1986.
5. Personal Communication between Dr. Richard T. Hart, Chairman, Department of Biomedical Engineering, Tulane University, New Orleans, LA and the author, 1999.
6. Fung, Y.C., Biomechanics: Mechanical Properties of Living Tissue, 2nd Ed., Springer-Verlag, New York, 1993.
7. Best, C.H. and Taylor, N. B. The Human Body: Its Anatomy and Physiology, 4th Ed., Holt, Rinehart, & Winston, 1963.
8. Gray, H., Anatomy: Descriptive and Surgical, 15th ed., Barnes and Noble Books, 1995.
9. Nordin, M. and Frankel, V., Basic Biomechanics of the Musculoskeletal System, Williams and Wilkins, 1989.
10. National Law Enforcement and Corrections Technology Center I National Institutes of Justice, "Selection and Application Guide to Police Body Armor," [http://www.ncjrs.org/txtfiles/169587.txt], Oct 1998.
11. Encyclopedia Brittani ca, "Bulletproof Vest," [http://www.britannica.com/bcom/eb/article/0/0,5716,18305+1+18046,00.html].
12. Office of Law Enforcement Standards I National Institutes of Justice, "Ballistic Resistance of Police Body Armor: NIJ Standard 0101.03," [http://www.oles.org/pdf/aaaad.pdf], April 1987.
1. DeMaio, M., Parks, S., et al., "Biomechanical Evaluation of Chest Body Armor," report, Armed Forces Institute of Pathology (AFIP).
89
13. Military Standard V50 Ballistic Test for Armor, MIL-STD-622E, January 1987.
14. Cunniff, P., "A Semiempirical Model for the Ballistic Impact Performance of TextileBased Personnel Armor," Textile Research Journal, v. 66, pp. 45-59, Jan 1996.
15. Vinson, J., Zukas, J., "On the Ballistic Impact of Textile Body Armor," Jouirnal of Applied Mechanics, v. 42, pp. 263-268, June 1975.
16. Roberts, S. B. and Chen, P.H., "Elastostatic Analysis of the Human Thoracic Skeleton,'' Journal ofBiomechanics, v. 3, pp. 527-545, 1970.
17. Hughes, T., Biomechanical Model of the Human Thorax for Impact Analysis, Master's Thesis, Naval Postgraduate School, Monterey, California, September 1999.
18. Andriacchi, T., Shultz, A., Belytschko, T., and Galante, J., "A Model for the Studies of the Mechanical Interaction between the Human Spine and Rib Cage,'' Journal of Biomechanics, v. 10, pp. 497-507, 1974.
19. Yogananda, N. and Pintar, F., "Biomechanics of Human Thoracic Ribs,'' Journal of Biomechanical Engineering, v. 120, pp. 100-104, Feb 1998.
20. Lee, K. S., Biomechanical Response of the Human Body inside a Military Vehicle Exposed to Mine Explosion, Master's Thesis, Naval Postgraduate School, Monterey, California, March 1999.
21. King, Q. M., Investigation of Biomechanical Response due to Fragment Impact on Ballistic Protective Helmet, Master's Thesis, Naval Postgraduate School, Monterey, California, March 1998.
22. Sundaram, S., and Feng, C., "Finite Element Analysis of the Human Thorax," Journal ofBiomechanics, v. 10, pp. 505-516, 1977.
23. Kolsky, H., Stress Waves in Solids, Dover, 1963.
24. Fliigge, W., Viscoelasticity, Blaisdell Publishing, 1967.
25. Lockett, F. J., Nonlinear Viscoelastic Solids, Academic Press, 1972.
90
APPENDIX A: PARAMETRIC STUDY RESULTS
In an attempt to understand the effects of the various parameters on the
biomechanical response of the thorax, the model parameters were changed individually
from the "standard" Kevlar vest and CBA plate model presented above. The results were
then compared to those obtained by DeMaio, et al [Ref. 13]. Significant changes
between the "standard" case and the results obtained with a parameter changed indicated
their importance to the model. The following is a listing of the various parameters that
were changed and the results obtained.
• Damping constant for damping discrete elements increased by four times
Sternum AcceleratiOn Spine Acceleration 2000
I-· ~lfA (#801, I .......... I-· ~lfA (#801, I
1500
-5
1000 -10
'.§ '.§
i 0
.Q
!-15
j j -20
-25
-500 -30
·. · ...... -1000
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -35
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time (ms) Time(ms)
91
• Damping constant for damping discrete elements increased by two times
S1emum Accelerarion Spine Acceleration 2000
I-· ~~(#801) I I-· Exp (#801) I FEA .........
1500
-5
-10 §
.~
I -15
-20
-25
-500
/ ......... --30
-1000 -35 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Time (ms) Time(ms)
• Damping constant for damping discrete elements decreased by half
Sternum AcceleraliOn Spine Acceleration 2000
I-· ~~(#801) I ....... I-· ~~(#801) I
1500
-5
1000 -10
§ §
-~ .~
I ~-15
§ <
'·.\\ ____
< -20
-25
..' -500
,. ....... / --30
·· ........ -1000 --35
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 08 1 1.2 1.4 1.6 1.8 Time (ms) Time (ms)
92
• Muscle material type changed from viscoelastic to elastic
Sternum Acceleration Spine Accslaration 2000
I-· m .. (#801)1 ........ I-· ~~(#801) I
1500
-5
-10 § §
i g ~ -15
§ < <
-20
-25
-500 __ .............. · -30
-1000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -350 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Time(ms) Time (ms)
• Muscle Young's Modulus increased five times
Sternum Acceleration Spine Acceter.ruion 2000
I-· m .. (#801)1 ......... I-· ~~(#801) I
1500
-5
1000 -10
§ §
I 5 500 ~-15
I I -20
-25
-500 -30
·· ....... -1000
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -35
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time(ms) Time(ms)
93
• Muscle density decreased three times
Sternum Acceleration Spine Acceleralion 2000
I-· ~~(#801) I ........ I-· ~~(#801) I
1500
-5
1000 -10
§ §
-~ .§ ]! 500 e-15
§ J <(
·•·· ... -20
•· ...... -25
-500 -30
......... -10000
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -35
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time (ms) Tine (ms)
• Sternal articular cartilage density decreased ten times
Stemum AcceleratiOn Spene Accelerauon 2000
I-· ~~(#801) I I-· Exp (#801) I FEA ..............
1500
-5
1000 -10
§ §
.§ c .2
j e-15
I -20
\ .... \ -25
-500 -30 ·. ·• .....
-1000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
-35 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Tine (ms) Time (ms)
94
• Sternal articular cartilage Young's Modulus increased ten times
Stemum Acceleration Spine Acceleration 2000
I-· ~~(#801) I ........... I-· ~~(#801) I
1500
-5
1000 -10
§ §
.§ -~ l'! 500 l'!-15
§ § .. \.\ .....
.. -20
-25
-500 __ ,,. .. ·
....... ·· -30 ... ·,.
'· •' -1000
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -350 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 rune(ms) Time (ms)
• Thoracic bones' densities set to 800 kg/m3
Stemum Acceleration Spine Acceleration 2000
I-· ~~(#801) I ......... I-· ~~(#801) I
1500
-5
1000 -10
§ §
.§ c ,g
I 500 ~ -15
§
\ ..•.. \ ..
-20
-25
-500
........ -30
·· ...... "" / -1000
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -350 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time(ms) Time (ms)
95
• Thoracic bones' Young's Modulus set to 12.l GP a
Stemum Acceleration Spine Acceleration 2000
J-· ~E'i (#801, I ....... I-· ~E'i (#801) I
1500
-5
-10 § § c -~ .2 1l! ~-15
§ ] < -20
-25
-500
,// -30 · . .......
-1000 -35 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Time (ms) Time(ms)
• Sternum bone density decreased 20%
Sternum Acceleration Spine AcceleraliOn 2000
I-· ~E'i (#801) I ........ I-· ~E'i (#801) I
1500
-5
1000 -10
§ §
~ -~ T!-15
j
\\ .. \
j -20
-25 ~
-500
_,.. ........ / -30 ·. ·· .....
-1000 -35 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
T<ne(ms) Time (ms)
96
• Intervertebral disc Young's Modulus decreased by ten times
Sternum AccelerariOn Spine Acceleration 2000
1-· ~~(#801) I 1-· Exp (#801) I FEA ........
1500
-5
-10
s s
I .§ °l!i-15
I ..
\ ............
-20
-25
-500
........... / -30
..... ... ··' -1000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
-35 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Time(ms) Time(ms)
• Intervertebral disc density increased by five times
Sternum Acceleration Spine Acceleration 2000
I-· ~~(#801) I ........ I-· ~~(#801) I
1500
-5
1000 -10
s s .§ .§
i ;-15
] .. \ .. \\
-20
-25
-500 ......... / -30
·· ........ . ... · -1000
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -350 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time(ms) Time (ms)
97
• Initial gap between sternum and vest removed
Stemum AcceleratlOn Spine Acceleralion 2000
I-· ~~(#801) I . . . .. . . . .
,_ . ~~(#801) I 1500
-5
1000 -10
§ §
.~ ~-- '··,··· ..•
.~
j 500 !-15
§
\\.\.
< -20
-25
-500
......... -30 ·. ·· ...... . ... ··
-1000 -35 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Time{ms) Time (ms)
• Contact elements directly between sternum and vest removed
S1emum Acceleration Spine Ac<:elera!!Oll 2000
1
_._ ~~(#801) I r----.:..·.:.:········ 1
_._ ~~(#801)! 1500
-5
1000 -10
§ c .2
I 500
:,..______, ......... . .. .. ··· .... _.-...
\'·· .. \. -20
-25
-500 -30
·. ·· ... '· -1000L---'---'----'--~--'---'"""'-'----'---'-----'
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time{ms)
98
:§ .§ ~ § <
:§ c .2 l'l § <
• Kevlar density increased five times
Sternum Accelerahon 2000
I -· _ ~~ (#801) I
1500
1000
500
\\· ...... . -500
......... -1000L---'----'---'----'---.1.._--l>~-'----'----'--__J
0 0.2 0.4 0.6 0.8 , 1.2 1.4 1.6 1.8 Time(ms)
:§ g
-5
-10
!!-15
1 -20
-25
-30
0.2
Spine Acceleration
......
0.4 0.6 0.8 , 1.2 Time (ms)
• Kevlar Young's Modulus increased five times
Sternum Acceleration Spine Accelerarion 2000
I-· ~~(#801) I ....... ······
1500
-5
-10 :§ c
"' !-ts §
\\· ......
< -20
-25
-500 -30 · .
........ -1000
0 0.2 0.4 0.6 0.8 , 1.2 1.4 -35
1.6 1.8 0 0.2 0.4 0.6 0.8 , 1.2 Time(rns) Time (ms)
99
I-·- ~~(#801) I
1.4 1.6 1.8
I-· ~~(#801) I
1.4 1.6 1.8
• CBA plate density increased two times
Sternum Acceleration 2000
Spine Acceleratoon
I-· ~~(#801) I ........ I-· ~~(#801) I
1500
-5
1000
.. ---... .......... -10 § §
·I • ..r \
~ 500 1!-15
~
\\· ..... I
-20
-25
' -500
.· -30
·· ...... .. .. -1000 -35
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 1.2 1.• 1.6 1.8 Time (ms) Time(ms)
• CBA plate Young's Modulus decreased two times
Sternum Acceleration Spfle AccelerarJOO 2000
I-· ~~(#801) I ........ I-· ~~(#801) I
1500
-5
-10 § § ~ .§ ~ 1!-15
i §
\ .... \ ..
< -20
-25
-500 -30
·· ..... -1000 -35
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time(ms) Time (ms)
100
2000
1500
1000
:§ g ~ 500
§ <
-500
-1000 0
2000
1500
1000
:§ ~
-I
-500
-1000 0
• Thorax and body annor dimensions increased 25%, Body annor thickness kept constant
Stemum AcceleratiOn Spine Acceleration
I-· ~~(#801) I I-· -5
-10 _.r--.. .... _.t""\ § ·.__..-.. .§
i!-15
j
\'\ ... -20
-25
...... / -30
·. . .. · ·· ..... ..J'· -35
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time(ms) Time(ms)
• Rib cross sections increased (diameters increased by 25%)
Sternum Acceleration Spine Acceleration
I-· ~~(#801) I ......... I-·
-5
-10 § § i!-15
§
\ .... \ <
-20
-25
.. /~ ._ .........
-30 ... · ... ,
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -350 0.2 0.4 0.6 0.8 1 1.2 1.4 Time(ms) Time (ms)
101
~~(#801) I
1.6 1.8
~~(#801) I
1.6 1.8
• Thorax dimensions increased by 25%, Body armor maintained at original dimensions
Sternum Accelerat.on Spine Accelerall0/1 2000
I-· ~~(#801) I I-· ~~(#801) I 1500
-5
1000 -10
§ §
~ .§ 1!! 1!!-15
I I -20
-25
-500
........ -30
·· ..... / -10000
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -35
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time (ms) Time (ms)
• Spring discrete element between muscle and ribs removed
Sternum Acceleration Spine AcceleraliOn 2000
I-· ~~(#801) I ........ I-· ~~(#801) I
1500
-5
1000 -10
§ § .§ .§
I 500 e-1s §
\ .. , __ \_ <
-20
-25
,. -500
_,.. ...... / -30
·· ..... -1000
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -35
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time (ms) Time (ms)
102
§
I ...
• Damper discrete element between muscle and ribs removed
Sternum Acceleration 2000
Spine Acceleration
I-· ~~(#801) I 1500
-5
1000
-10 .. ,.,....__,,_ .... __ .,.,,,.. .. _ §
· ..... ,,r-,· ..... :s 500 ~-15
§
\\\ ..
... -20
-25
-500 ........ ,..-·· -30 ·. ·· ..... ... ... . ..
-1000 0.6 1 1.6 1.8
-35 0.6 0 0.2 0.4 0.8 1.2 1.4 0 0.2 0.4 0.8 1
Time(ms) Time(ms)
• Spring discrete elements and muscles removed from model
x 104 Sternum Acceleration Spine Acceleralion 4
-2
-3
-4 0
I\ h I td n
vvv\
0.2 0.4
I-·
Ii
~
0.6 0.8 1 1.2 1.4 1.6 Time(ms)
~~(#801) I
-5
-10 § .§ - ~-15
~ -20
-25
-30
1.8 -350 0.2 0.4 0.6 0.8 1 Time(ms)
103
I -- ~~(#801) I
1.2 1.4 1.6 1.8
I-· ~~(#801) I
1.2 1.4 1.6 1.8
• Damper and spring discrete elements between muscle and ribs removed
Sternum Acceleration 2000
Spine Acceleralion
J
I-· ~E'i (#801) I ........... I-· ~~(#801) I
1500
-5
1000
,._ ~, I -10
§ .-. § c c ,Q .2 1!! 500 ,.. 1!! -15
j j -20 ,,.,.-
' / -25
-500 'f ~~ .. ·. -30
-1000 0.4 0.6 0.8 1 1.2 1.6 1.8
-35 0.4 0.6 0.8 1 1.6 1.8 0 0.2 1.4 0 0.2 1.2 1.4
Time(ms) Time (ms)
• Point of impact of projectile along sternum moved inferiorly by 6 cm
Slemum Acceleration Spne Acceleratl0!1 2000
I-· ~E'i (#801) I ........ I-· ~~(#801) I
1500
-5
1000 -10
§ §
i 5 !-15
j §
\,.,\ ... <
-20
-25
-500
........... / -30 ·. ·-...... •'
-1000 1.6
-35 0.4 1 1.6 1.8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.8 0 0.2 0.6 0.8 1.2 1.4
Time(ms) Time (ms)
104
:§
I
:§
2000
• Body armor dimensions increased to 25 cm by 18 cm, thorax dimensions constant, musculature between vest and thorax increased; densities of the CBA and Kevlar are scaled to maintain same mass for body armor; number of damper discrete elements increased
Sternum Acceleration Spine Acceleration
1-· ~~(#801) I ······· ... 1-· ~~(#801) I
1500
-5
1000 -10 ... ----.. ... __ ,.,... :§
0
500 '·-..... •....•. .9 °!!!-15
j
\., .. \. -20
-25
............... · -30
.......... .,,··
-500
-1000L--'---"---"---'---'---""""'-'---'----''----' -35 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 1.2 1.4
Time(ms) Time(ms)
• Body armor dimensions increased to 25 cm by 18 cm, thorax dimensions constant, musculature between vest and thorax increased; densities of the CBA plate and Kevlar are not scaled; number of damper discrete elements increased
Sternum Acceleration Spine Acceleration 2000,-r--r--r--r--.-----i.--""';:::::!c:::::::::::::!=:::::::::=::-i 1-·- ~~(#801) I ........... 1500
-5
-10
1.6 1.8
I soo ............. g ~-15
j
\.\ ..... ~
-20
-25
-500 • -30
·. ·· ..... -1000 L--'---'---'---'---'---=--''----'---'---'
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time(ms) Time(ms)
105
• Body armor dimensions increased to 25 cm by 18 cm, thorax dimensions constant, musculature between vest and thorax increased; densities of the CBA plate and Kevlar are not scaled; original number of dampers used
S1emum Acceleration Spine Acceleration 2000
I-· ~~(#801) I .......
,_. ~~(#801) I 1500
-5
-10 §
.~
··,··· ... "§ 500 -15
I
\\\\ -20
-25
-500
....... · -30
·· ..... / -10000
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -35
0 0.2 0.4 0.6 0.8 , 1.2 1.4 1.6 1.8 Tirne(ms) Time (ms)
106
APPENDIX B: VISCOELASTIC SOLIDS
The use of a time-dependent shear modulus in the muscle elements of the thorax
model was required to adequately model its viscous effects. In order to understand the
theory behind the use of the equation to create the time-dependent response of the shear
modulus, it is necessary to understand the modifications necessary to Hooke's Law. (See
Refs. 24, 25 and 26 for a discussion on viscoelasticity.)
For a viscous material, the relationship between strain, s, and stress, cr, can no
longer be represented by the equation:
a=E * 8 (Hooke's Law)
Instead, various models are created to represent the behavior of a viscoelastic material.
Several of these are depicted in Figure 56 below. By placing a combination of springs
and "dashpots," modeled by the dampers, in series and in parallel, it is possible to create
the desired behavior of the solid.
Voight Solid Maxwell Solid General Solid
Figure 56: Models of Viscoelastic Solids. From Ref. [24]
107
The viscoelasticity represented by the DYNA3D material model is represented in
Figure 57 below.
Figure 57: Model ofDYNA3D Viscoelastic Solid
In order to determine the behavior of this model, the stress-strain relationships
must be determined. In general, the behavior of a massl~ss, linear spring with a spring
constant, K, follows Hooke's Law,
a=K * 8 ,
with cr as the stress and E as the strain. [Ref. 25] The relationship between stress and
strain in the dashpots is as follows,
a=µ*&,
withµ as the viscosity of the dashpot and i = de. [Ref. 25] dt
In order to determine the time-dependent shear modulus, the first step is to find
the stress-strain relationship for the model presented in Figure 57. Since the model has
elements both in series and in parallel, it is essential to know how stresses and strains
combine for these combinations. For a dashpot and spring in series, illustrated by the
108
Maxwell solid in Figure 56, the stress in the series is equal to the stress in each element
and the strain is the sum of the strain in the two elements, such as a = a K = aµ and
& = & K + & µ , with K as the spring constant and µ as the dashpot viscosity. For a dashpot
and spring in parallel, illustrated by the Voight solid in Figure 56, the stress is equal to
the sum of the stresses in each element and the strain is the equal to the strain in each
individual element, such that a = a K +aµ and & = & K = & µ . [Ref. 26]
For the model utilized by DYNA3D, the stresses in each branch must be
computed individually and then combined according to the relationships presented above.
Let the top branch, with the singular spring element, be branch A and let the bottom
branch be branch B. First, compute the stresses and strains for branch B, according to the
Maxwell model. Since & = & K + & µ , a = K * s , and CJ' = µ * & , the following
relationship can be determined for branch B:
~'+ G~G. =i:, orrewritten, a,=(c, G~G}
For Branch A, Hooke's Law applies and CJ' A = G"" * 8 A •
Placing the elements in parallel, CJ' = CJ' A+ CJ' 8
and therefore, 0- = 0-A + 0-8
•
Combining the terms yields the following:
Now,
u +(G.~G.Jc:T,=µf,+G. * &,·
109
So,
which is the stress-strain relationship for this model.
In order to find the shear modulus of the material, which is dependent upon the
spring constants and viscosity, a simplification and several substitutions are required.
First, the parameter, µ , can be represented as 1, the retardation time for the model. Go-Goo
Also, substitute in £ = £ 0 [U(t )] and & = &
0 [8(t )] . These parameters represent the
application of a strain to the Maxwell solid. U(t) is the unit step function and o(t) is the
I
delta-dirac function. Now, integrating with the integration factor, er , gives the
following:
<Y *if< = &o' (G ,)J;; [0(1•)}11•+ &o * (Go~ G .)* G. J;; [u(1')}11' 0 0
110
Using the relationships that J J(t 1)[u&1 -1J}tt1= [U(t-tJ]f J(t')dt' and -oo ti
f J(t')[o&1 -1J}tt'= 1&Ju(t-t1)], it follow that
Simplifying leads to
and
Thus, using a generalized form of Hooke's Law, the modulus must be
G (t )=Goo + ( G 0 - G 00
)e -flt , with fJ = !_. 1:
111
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112
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